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A318684
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Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums.
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18
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1, 1, 1, 3, 3, 5, 8, 11, 14, 20, 28, 35, 48, 61, 79, 105, 129, 162, 208, 257, 318, 404, 489, 600, 732, 896, 1075, 1315, 1576, 1895, 2272, 2715, 3217, 3851, 4537, 5377, 6353, 7484, 8765, 10314, 12044, 14079, 16420, 19114, 22184, 25818, 29840, 34528, 39903, 46030
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(9) = 20 split partitions:
(9)
(81) (8)(1)
(72) (7)(2)
(63) (6)(3)
(54) (5)(4)
(432) (43)(2) (4)(3)(2)
(621) (62)(1) (6)(2)(1) (6)(21)
(531) (53)(1) (5)(3)(1) (5)(31)
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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], OrderedQ[Total/@#, Greater]&]], {y, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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