The fxt demos: integer sequences

Directory seq: Integer sequences by OEIS number, see http://oeis.org/.
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-restrpref.h (fxt/src/comb/composition-nz-restrpref.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 perm-restrpref.h (fxt/src/comb/perm-restrpref.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) num2str.h (fxt/src/aux1/num2str.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)

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) perm-restrpref.h (fxt/src/comb/perm-restrpref.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)

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-lex2.h (fxt/src/comb/perm-lex2.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) bitzip-pairs.h (fxt/src/bits/bitzip-pairs.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)

A215327-out.txt is the output of A215327-demo.cc.
OEIS sequence A215327: smooth necklaces with 3 colors. Also A215328: smooth Lyndon words with 3 colors. Also A215329: smooth necklaces, 4 colors. Also A215330: smooth Lyndon words, 4 colors. Also A215331: smooth necklaces, 5 colors. Also A215332: smooth Lyndon words, 5 colors. Also A215333: smooth necklaces, 7 colors. Also A215334: smooth Lyndon words, 7 colors. Also A208772: cyclically smooth necklaces, 3 colors. Also A208773: cyclically smooth necklaces, 4 colors. Also A208774: cyclically smooth necklaces, 5 colors. Also A208775: cyclically smooth necklaces, 6 colors. Also A208776: cyclically smooth necklaces, 7 colors. Also A208777: array (cyclically smooth necklaces of k colors as column k). Also A215335: cyclically smooth Lyndon words, 3 colors. Also A215336: cyclically smooth Lyndon words, 4 colors. Also A215337: cyclically smooth Lyndon words, 5 colors. Also A215338: cyclically smooth Lyndon words, 7 colors.
The demo uses the functions from necklace.h (fxt/src/comb/necklace.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-lex.h (fxt/src/comb/mixedradix-lex.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.
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)

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)