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A317715
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Number of ways to split an integer partition of n into consecutive subsequences with equal sums.
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22
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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
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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