Find a list of all files in this directory here. An index of all topics is here

You may want to look at the outputs first.

A000793-out.txt is the output of A000793-demo.cc.

**
OEIS sequence A000793:
Landau's function g(n): largest order of permutation of n elements.
Equivalently, largest lcm of (the parts of) partitions of n.
Also sequence A213206.
**

The demo uses the functions from
composition-nz-prefix-cond.h (fxt/src/comb/composition-nz-prefix-cond.h)
gcd.h (fxt/src/aux0/gcd.h)

A003040-out.txt is the output of A003040-demo.cc.

**
OEIS sequence A003040:
Highest degree of an irreducible representation of symmetric group S_n of degree n.
Cf. sequence A082914:
Minimum product of hook lengths of a partition of n.
**

The demo uses the functions from
partition-dist-d-asc.h (fxt/src/comb/partition-dist-d-asc.h)
partition-hook-prod.h (fxt/src/comb/partition-hook-prod.h)
partition-conj.h (fxt/src/comb/partition-conj.h)
factorial.h (fxt/src/aux0/factorial.h)

A003043-out.txt is the output of A003043-demo.cc.

**
OEIS sequence A003043:
Number of Hamiltonian paths (or Gray codes) on n-cube with a marked starting node.
Computation as Permutations with restricted prefixes.
Also A059783: paths from vec(0) to vec(1).
**

The demo uses the functions from
perm1-prefix-cond.h (fxt/src/comb/perm1-prefix-cond.h)

A005351-out.txt is the output of A005351-demo.cc.

**
OEIS sequence A005351:
Base -2 representation for n reinterpreted as binary.
Also sequence A005352:
Base -2 representation of -n reinterpreted as binary.
**

The demo uses the functions from
negbin.h (fxt/src/bits/negbin.h)

A005576-out.txt is the output of A005576-demo.cc.

**
OEIS sequence A005576:
The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r.
**

The demo uses the functions from
partition-dist-desc.h (fxt/src/comb/partition-dist-desc.h)

A005943-out.txt is the output of A005943-demo.cc.

**
OEIS sequence A005943:
Length-n subwords of the Golay-Rudin-Shapiro (GRS) sequence.
**

The demo uses the functions from
grsnegative.h (fxt/src/bits/grsnegative.h)
bitarray.h (fxt/src/ds/bitarray.h)
print-bin.h (fxt/src/bits/print-bin.h)

A006951-out.txt is the output of A006951-demo.cc.

**
OEIS sequence A006951:
Number of conjugacy classes in GL(n,2).
Computed by a summation over integer partitions of n.
Also OEIS sequences "Number of conjugacy classes in GL(n,q)":
q=3: A006952, q=4: A049314, q=5: A049315, q=7: A049316, q=8: A182603,
q=9: A182604, q=11: A182605, q=13: A182606, q=16: A182607, q=17: A182608,
q=19: A182609, q=23: A182610, q=25: A182611, q=27: A182612.
Non prime powers:
q=6: A221578, q=10: A221579, q=12: A221580, q=14: A221581,
q=15: A221582, q=18: A221583, q=20: A221584.
**

The demo uses the functions from
partition-desc.h (fxt/src/comb/partition-desc.h)
ipow.h (fxt/src/aux0/ipow.h)

A007608-out.txt is the output of A007608-demo.cc.

**
OEIS sequence A007608:
Numbers in base -4.
Also A212526: negative numbers in base -4.
**

The demo uses the functions from
radix-m4.h (fxt/src/bits/radix-m4.h)
num2str.h (fxt/src/aux1/num2str.h)

A039724-out.txt is the output of A039724-demo.cc.

**
OEIS sequence A039724:
Numbers in base -2.
Also A212529: negative numbers in base -2.
**

The demo uses the functions from
negbin.h (fxt/src/bits/negbin.h)
num2str.h (fxt/src/aux1/num2str.h)

A042942-out.txt is the output of A042942-demo.cc.

**
Sequence A042942 of the OEIS,
related to the Oldenburger-Kolakoski sequence (A000002).
Cf. https://en.wikipedia.org/wiki/Kolakoski_sequence
Algorithm by David Eppstein,
see http://11011110.livejournal.com/336374.html
**

The demo uses the functions from
kolakoski-seq.h (fxt/src/bits/kolakoski-seq.h)

A062200-out.txt is the output of A062200-demo.cc.

**
OEIS sequence A062200:
Compositions of n where adjacent parts have different parity.
**

The demo uses the functions from
composition-nz.h (fxt/src/comb/composition-nz.h)

A066411-out.txt is the output of A066411-demo.cc.

**
OEIS sequence A066411:
Number of sums of c_k * (n choose k) where the c_k are a permutation of 0 through n.
Sequence A126972: permutations of [1..n], sum(k=1..n, (pi(k)-k)^2).
Sequence A189043: permutations of [1..n], sum(k=1..n, k^2 * pi(k) ).
**

The demo uses the functions from
perm-trotter.h (fxt/src/comb/perm-trotter.h)
bitarray.h (fxt/src/ds/bitarray.h)
binomial.h (fxt/src/aux0/binomial.h)

A069999-2-out.txt is the output of A069999-2-demo.cc.

**
OEIS sequence A069999:
Number of possible dimensions for commutators of n X n matrices.
Computation using a convolution over sets.
**

The demo uses the functions from
fxtio.h (fxt/src/fxtio.h)

A069999-out.txt is the output of A069999-demo.cc.

**
OEIS sequence A069999:
Number of possible dimensions for commutators of n X n matrices.
Also sequence A111212.
**

The demo uses the functions from
partition-asc-subset-lex.h (fxt/src/comb/partition-asc-subset-lex.h)
bitarray.h (fxt/src/ds/bitarray.h)

A080936-out.txt is the output of A080936-demo.cc.

**
OEIS sequence A080936:
Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n and height k (1<=k<=n).
Same as: Catalan restricted growth strings (RGS) by max digit.
**

The demo uses the functions from
catalan-rgs-subset-lex.h (fxt/src/comb/catalan-rgs-subset-lex.h)

A100749-out.txt is the output of A100749-demo.cc.

**
OEIS sequence A100749:
number of compositions of n having k odd parts.
**

The demo uses the functions from
composition-nz.h (fxt/src/comb/composition-nz.h)

A175498-out.txt is the output of A175498-demo.cc.

**
OEIS sequence A175498:
Greedily choose next n (minimal) such that all differences in prefix are distinct.
**

The demo uses the functions from
bitarray.h (fxt/src/ds/bitarray.h)

A177505-out.txt is the output of A177505-demo.cc.

**
OEIS sequence A177505:
Base 2i representation of n reinterpreted in base 4.
**

The demo uses the functions from
radix-2i.h (fxt/src/bits/radix-2i.h)
radix-m4.h (fxt/src/bits/radix-m4.h)
bitzip-pairs.h (fxt/src/bits/bitzip-pairs.h)

A178514-out.txt is the output of A178514-demo.cc.

**
OEIS sequence A178514:
genus of derangements.
Also A178515: genus of involutions.
Also A178516: genus of up-down permutations.
Also A177267: genus of all permutations.
Also A178517: genus of non-derangement permutations.
Cf. comb/perm-genus-demo.cc
**

The demo uses the functions from
perm-genus.h (fxt/src/perm/perm-genus.h)
perm1-prefix-cond.h (fxt/src/comb/perm1-prefix-cond.h)

A178715-out.txt is the output of A178715-demo.cc.

**
OEIS sequence A178715:
Maximal value of prod(k=1..m, p_k-1 ) over all partitions
p_1 + p_2 + ... + p_m of n+1.
**

The demo uses the functions from
partition-asc.h (fxt/src/comb/partition-asc.h)

A179009-out.txt is the output of A179009-demo.cc.

**
OEIS sequence A179009:
Maximally refined partitions into distinct parts.
A partition (into distinct parts) can be refined if any part
can be split into two parts not in the partition.
A maximally refined partition cannot be refined.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)

A179080-out.txt is the output of A179080-demo.cc.

**
OEIS sequence A179080:
Integer partitions into distinct parts where adjacent parts have different parity.
Also A179049 and A218355: first part respectively odd and even.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)

A182039-out.txt is the output of A182039-demo.cc.

**
OEIS sequence A182039:
Number of orthogonal 2 x 2 matrices M in the ring Z/nZ.
**

A182372-out.txt is the output of A182372-demo.cc.

**
OEIS sequence A182372:
Number of distinct sets of non-negative integers with perimeter n.
**

A186053-out.txt is the output of A186053-demo.cc.

**
OEIS sequence A186053:
Smallest perimeter among all sets of non-negative integers whose volume is n.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)
partition-boundary.h (fxt/src/comb/partition-boundary.h)

A187081-out.txt is the output of A187081-demo.cc.

**
OEIS sequence A187081: sand piles by height.
Same as: compositions of n where the first and the last parts are 1 and
the absolute difference between consecutive parts is <=1.
Also A186084: sand piles by base length.
Also A186085: sand piles with n grains.
Also A187080: fountains of coins by height.
Also A047998: fountains of coins by base length.
Also A005169: fountains of n coins.
**

The demo uses the functions from
composition-nz-numparts.h (fxt/src/comb/composition-nz-numparts.h)

A191755-out.txt is the output of A191755-demo.cc.

**
OEIS sequence A191755:
Binary self-shuffle words.
**

The demo uses the functions from
combination-colex.h (fxt/src/comb/combination-colex.h)
ruler-func.h (fxt/src/comb/ruler-func.h)
bitarray.h (fxt/src/ds/bitarray.h)

A206464-out.txt is the output of A206464-demo.cc.

**
OEIS sequence A206464:
Number of length-n Catalan-RGS (restricted growth strings) such that
the RGS is a valid mixed radix number in falling factorial basis.
**

The demo uses the functions from
catalan-rgs-subset-lex.h (fxt/src/comb/catalan-rgs-subset-lex.h)

A206702-out.txt is the output of A206702-demo.cc.

**
OEIS sequence A206702:
Number of subsets of S of { 0, 1, 2, ..., n-1 } such that
for all u, v in S u + v is not in S.
**

The demo uses the functions from
subset-lex.h (fxt/src/comb/subset-lex.h)

A207018-out.txt is the output of A207018-demo.cc.

**
OEIS sequence A207018:
Number of permutations with major index equal to inversion number.
**

The demo uses the functions from
perm-lex.h (fxt/src/comb/perm-lex.h)
permq.h (fxt/src/perm/permq.h)

A209411-out.txt is the output of A209411-demo.cc.

**
OEIS sequence A209411:
Number of 2 x 2 matrices M such that M*transpose(M) == 0 (mod n).
**

A212494-out.txt is the output of A212494-demo.cc.

**
OEIS sequence A212494:
Base 2i representation of n.
Also A212542: base 2i representation of negative numbers.
**

The demo uses the functions from
radix-2i.h (fxt/src/bits/radix-2i.h)
radix-m4.h (fxt/src/bits/radix-m4.h)
num2str.h (fxt/src/aux1/num2str.h)

A213243-out.txt is the output of A213243-demo.cc.

**
OEIS sequence A213243:
Number of nonzero elements in GF(2^n) that are cubes.
Also A213244: 5th powers.
Also A213245: 7th powers.
Also A213246: 9th powers.
Also A213247: 11th powers.
Also A213248: 13th powers.
**

The demo uses the functions from
gf2n.h (fxt/src/bpol/gf2n.h)
gf2n.cc (fxt/src/bpol/gf2n.cc)
bitarray.h (fxt/src/ds/bitarray.h)

A217262-out.txt is the output of A217262-demo.cc.

**
OEIS sequence A217262:
Delta sequence for binary words in a minimal-change order (subset-lex Gray code).
**

The demo uses the functions from
bit-sl-gray.h (fxt/src/bits/bit-sl-gray.h)
bit2pow.h (fxt/src/bits/bit2pow.h)

A217605-out.txt is the output of A217605-demo.cc.

**
OEIS sequence A217605:
Number of partitions that are fixed points of a certain map.
**

The demo uses the functions from
partition.h (fxt/src/comb/partition.h)

A218293-out.txt is the output of A218293-demo.cc.

**
OEIS sequence A218293:
standard Young tableaux with shapes corresponding to partitions into distinct parts.
Also OEIS sequences
A000085 (all tableaux, d=0),
A225121 (tableaux for partitions into distinct parts with minimal difference 2, d=0),
**

The demo uses the functions from
partition-dist-d-asc.h (fxt/src/comb/partition-dist-d-asc.h)
partition-hook-prod.h (fxt/src/comb/partition-hook-prod.h)
partition-conj.h (fxt/src/comb/partition-conj.h)
factorial.h (fxt/src/aux0/factorial.h)

A218396-out.txt is the output of A218396-demo.cc.

**
OEIS sequence A218396:
compositions into distinct (nonzero) Fibonacci numbers.
Also A032021: compositions into distinct odd numbers.
Also A000119: partitions into distinct Fibonacci numbers.
Also A000700: partitions into distinct odd numbers.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)
fibonacci.h (fxt/src/aux0/fibonacci.h)
bsearch.h (fxt/src/sort/bsearch.h)

A218694-out.txt is the output of A218694-demo.cc.

**
OEIS sequence A218694:
Compositions of n where adjacent parts are distinct (Carlitz compositions)
and all parts are odd.
**

The demo uses the functions from
composition-nz-carlitz.h (fxt/src/comb/composition-nz-carlitz.h)

A218757-out.txt is the output of A218757-demo.cc.

**
OEIS sequence A218757:
number of length-n ascent sequences without flat steps containing k zeros.
**

The demo uses the functions from
ascent-nonflat-rgs.h (fxt/src/comb/ascent-nonflat-rgs.h)
word-stats.h (fxt/src/comb/word-stats.h)

A225084-out.txt is the output of A225084-demo.cc.

**
OEIS sequence A225084:
number of compositions of n with maximal up-step k.
OEIS sequence A225085:
number of compositions of n with maximal up-step <= k.
Cf. A003116 (max up-step 1) and A224959 (max up-step 2).
**

The demo uses the functions from
composition-nz.h (fxt/src/comb/composition-nz.h)

A225095-out.txt is the output of A225095-demo.cc.

**
OEIS sequence A225095:
Number of maximums over all length-n sequences on {1,2,...,n}.
**

The demo uses the functions from
mixedradix.h (fxt/src/comb/mixedradix.h)

A225616-out.txt is the output of A225616-demo.cc.

**
OEIS sequence A225616:
Tableaux of size n with major index equal to 1 mod n.
A descent in a standard Young tableau is a entry i such that i+1 lies
strictly below and weakly left of i.
The major index is the sum of all such i.
Also sequences A161125 (descent numbers), A225617 (strict inversions),
and A225618 (weak inversions).
**

The demo uses the functions from
young-tab-rgs.h (fxt/src/comb/young-tab-rgs.h)
young-tab-rgs-descents.h (fxt/src/comb/young-tab-rgs-descents.h)
print-young-tab-rgs-aa.cc (fxt/src/comb/print-young-tab-rgs-aa.cc)
is-shifted-young-tab-rgs.h (fxt/src/comb/is-shifted-young-tab-rgs.h)

A226893-out.txt is the output of A226893-demo.cc.

**
OEIS sequence A226893:
Number of binary Lyndon words of length n having a conjugate at Hamming distance 2.
**

The demo uses the functions from
bit-necklace.h (fxt/src/bits/bit-necklace.h)
bitrotate.h (fxt/src/bits/bitrotate.h)
bitcount.h (fxt/src/bits/bitcount.h)

A227344-out.txt is the output of A227344-demo.cc.

**
OEIS sequence A227344:
Triangle, partitions into distinct parts by perimeter.
Also A227345:
Triangle, partitions into distinct parts by boundary size.
Also A227426:
Partitions into distinct parts with maximal perimeter.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)
partition-boundary.h (fxt/src/comb/partition-boundary.h)

A240949-out.txt is the output of A240949-demo.cc.

**
Integer partitions where the parities of all even parts must be
equal and the parities of all odd parts must be equal.
Cf. OEIS sequence A240949.
**

The demo uses the functions from
partition-asc.h (fxt/src/comb/partition-asc.h)

A247386-out.txt is the output of A247386-demo.cc.

**
OEIS sequence A247386:
Sum of the major index over all standard Young tableaux with n cells.
**

The demo uses the functions from
young-tab-rgs.h (fxt/src/comb/young-tab-rgs.h)
young-tab-rgs-descents.h (fxt/src/comb/young-tab-rgs-descents.h)

A249872-out.txt is the output of A249872-demo.cc.

**
OEIS sequence A249872:
Number of iterations to reach a final state for an n X n lattice of sand piles on a torus.
Also A293452: number of iterations for an n X k lattice.
**

The demo uses the functions from
array2d.h (fxt/src/ds/array2d.h)

A259095-out.txt is the output of A259095-demo.cc.

**
OEIS sequence A259095:
Number of arrangements of n pennies in rows, r pennies in the bottom row, and each higher row consisting of contiguous pennies.
Computed via integer partitions into distinct parts as ascending list of parts.
**

The demo uses the functions from
partition-dist-asc.h (fxt/src/comb/partition-dist-asc.h)

A276691-out.txt is the output of A276691-demo.cc.

**
A276691: Sum of maximum subrange sum over all length-n arrays of {+1, -1}.
**

The demo uses the functions from
ruler-func.h (fxt/src/comb/ruler-func.h)
max-subrange-sum.h (fxt/src/comb/max-subrange-sum.h)

A278479-out.txt is the output of A278479-demo.cc.

**
OEIS sequence A278479:
Least k such that the 2-adic valuation of the k-th partition number is n.
**

The demo uses the functions from
bitlow.h (fxt/src/bits/bitlow.h)
bitsperlong.h (fxt/src/bits/bitsperlong.h)

A309807-out.txt is the output of A309807-demo.cc.

**
OEIS sequence A309807:
Number of permutations sigma of [n] such that sigma(k)/k > sigma(k+1)/(k+1) for 1 <= k <= n-1.
**

The demo uses the functions from
perm1-prefix-cond.h (fxt/src/comb/perm1-prefix-cond.h)