A318683 Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums.

1, 1, 1, 2, 2, 3, 5, 5, 7, 8, 12, 12, 18, 18, 26, 27, 37, 38, 53, 54, 73, 76, 100, 104, 136, 142, 183, 192, 244, 256, 327, 340, 424, 448, 558, 585, 722, 760, 937, 983, 1195, 1260, 1544, 1610, 1943, 2053, 2480, 2590, 3107, 3264, 3927, 4106, 4874, 5120, 6134, 6378

Offset

0,4

Links

Table of n, a(n) for n=0..55.

Example

The a(12) = 18 constant-sum split partitions:
  (12)
  (7,5)
  (8,4)
  (9,3)
  (10,2)
  (11,1)
  (5,4,3)
  (6,4,2)
  (6,5,1)
  (7,3,2)
  (7,4,1)
  (8,3,1)
  (9,2,1)
  (6)(4,2)
  (6)(5,1)
  (5,4,2,1)
  (6,3,2,1)
  (6)(3,2,1)

Mathematica

comps[q_]:=Table[Table[Take[q, {Total[Take[c, i-1]]+1, Total[Take[c, i]]}], {i, Length[c]}], {c, Join@@Permutations/@IntegerPartitions[Length[q]]}];
Table[Sum[Length[Select[comps[y], SameQ@@Total/@#&]], {y, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}]

Crossrefs

Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A318684, A319794.

Sequence in context: A113827 A033189 A008507 * A028364 A239482 A280470

Adjacent sequences: A318680 A318681 A318682 * A318684 A318685 A318686

Keyword

nonn

Author

Gus Wiseman, Sep 29 2018

Status

approved