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 A317715 Number of ways to split an integer partition of n into consecutive subsequences with equal sums. 22
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 2 15:42 EDT 2023. Contains 363098 sequences. (Running on oeis4.)