A317715 Number of ways to split an integer partition of n into consecutive subsequences with equal sums.

1, 1, 3, 4, 9, 8, 21, 16, 39, 38, 64, 57, 146, 102, 186, 211, 352, 298, 593, 491, 906, 880, 1273, 1256, 2444, 1998, 3038, 3277, 4861, 4566, 7710, 6843, 10841, 10742, 14966, 15071, 24499, 21638, 31334, 32706, 47157, 44584, 67464, 63262, 91351, 94247, 125248

Offset

0,3

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 0..500

Gus Wiseman, The a(8) = 39 constant-sum split partitions.

Gus Wiseman, The a(10) = 64 constant-sum split partitions.

Gus Wiseman, The a(12) = 146 constant-sum split partitions.

Example

The a(4) = 9 constant-sum split partitions:
  (4),
  (31),
  (22), (2)(2),
  (211), (2)(11),
  (1111), (11)(11), (1)(1)(1)(1).
The a(6) = 21 constant-sum split partitions:
  (6),
  (51),
  (42),
  (411),
  (33), (3)(3),
  (321), (3)(21),
  (3111), (3)(111),
  (222), (2)(2)(2),
  (2211), (2)(2)(11),
  (21111), (21)(111), (2)(11)(11),
  (111111), (111)(111), (11)(11)(11), (1)(1)(1)(1)(1)(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, IntegerPartitions[n]}], {n, 10}]

Crossrefs

Cf. A000041, A001970, A063834, A316223, A317545, A317546, A319001.

Cf. A316245, A317508, A318434, A318683, A318684, A319794.

Sequence in context: A217578 A280616 A317099 * A305551 A306018 A076120

Adjacent sequences: A317712 A317713 A317714 * A317716 A317717 A317718

Keyword

nonn

Author

Gus Wiseman, Sep 29 2018

Extensions

a(16)-a(46) from Hiroaki Yamanouchi, Oct 02 2018

Status

approved