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 A318683 Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums. 16
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 2 14:52 EDT 2023. Contains 363097 sequences. (Running on oeis4.)