// output of ./demo/seq/A187081-demo.cc:
// Description:
//% 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.

arg 1: 10 == n  [Compositions of n (n>=1)]  default=10
arg 2: 1 == sq  [Whether to generate sandpiles (else fountains of coins)]  default=1
arg 3: 1 == hq  [Whether to gather stats about height (else about base length)]  default=1
 3     1:    [ 1 2 3 2 1 1 ]
 2     2:    [ 1 2 2 2 2 1 ]
 3     3:    [ 1 1 2 3 2 1 ]
 2     4:    [ 1 2 2 2 1 1 1 ]
 2     5:    [ 1 2 2 1 2 1 1 ]
 2     6:    [ 1 2 1 2 2 1 1 ]
 2     7:    [ 1 1 2 2 2 1 1 ]
 2     8:    [ 1 2 2 1 1 2 1 ]
 2     9:    [ 1 2 1 2 1 2 1 ]
 2    10:    [ 1 1 2 2 1 2 1 ]
 2    11:    [ 1 2 1 1 2 2 1 ]
 2    12:    [ 1 1 2 1 2 2 1 ]
 2    13:    [ 1 1 1 2 2 2 1 ]
 2    14:    [ 1 2 2 1 1 1 1 1 ]
 2    15:    [ 1 2 1 2 1 1 1 1 ]
 2    16:    [ 1 1 2 2 1 1 1 1 ]
 2    17:    [ 1 2 1 1 2 1 1 1 ]
 2    18:    [ 1 1 2 1 2 1 1 1 ]
 2    19:    [ 1 1 1 2 2 1 1 1 ]
 2    20:    [ 1 2 1 1 1 2 1 1 ]
 2    21:    [ 1 1 2 1 1 2 1 1 ]
 2    22:    [ 1 1 1 2 1 2 1 1 ]
 2    23:    [ 1 1 1 1 2 2 1 1 ]
 2    24:    [ 1 2 1 1 1 1 2 1 ]
 2    25:    [ 1 1 2 1 1 1 2 1 ]
 2    26:    [ 1 1 1 2 1 1 2 1 ]
 2    27:    [ 1 1 1 1 2 1 2 1 ]
 2    28:    [ 1 1 1 1 1 2 2 1 ]
 2    29:    [ 1 2 1 1 1 1 1 1 1 ]
 2    30:    [ 1 1 2 1 1 1 1 1 1 ]
 2    31:    [ 1 1 1 2 1 1 1 1 1 ]
 2    32:    [ 1 1 1 1 2 1 1 1 1 ]
 2    33:    [ 1 1 1 1 1 2 1 1 1 ]
 2    34:    [ 1 1 1 1 1 1 2 1 1 ]
 2    35:    [ 1 1 1 1 1 1 1 2 1 ]
 1    36:    [ 1 1 1 1 1 1 1 1 1 1 ]
  stats:  0 1 33 2 0 0 0 0 0 0 0 
 ct=36