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A319794
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Number of ways to split a strict integer partition of n into consecutive subsequences with weakly decreasing sums.
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17
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1, 1, 1, 3, 3, 5, 9, 11, 15, 20, 31, 37, 52, 64, 85, 111, 141, 175, 225, 279, 346, 437, 532, 654, 802, 979, 1182, 1438, 1740, 2083, 2502, 2996, 3565, 4245, 5043, 5950, 7068, 8303, 9772, 11449, 13452, 15681, 18355, 21338, 24855, 28846, 33509, 38687, 44819, 51644
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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(6) = 9 split partitions:
(6)
(51) (5)(1)
(42) (4)(2)
(321) (32)(1) (3)(21) (3)(2)(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], OrderedQ[Total/@#, GreaterEqual]&]], {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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