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A316245
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Number of ways to split an integer partition of n into consecutive subsequences with weakly decreasing sums.
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27
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1, 1, 3, 6, 14, 25, 52, 89, 167, 279, 486, 786, 1322, 2069, 3326, 5128, 8004, 12055, 18384, 27203, 40588, 59186, 86645, 124583, 179784, 255111, 362767, 509319, 715422, 993681, 1380793, 1899630, 2613064, 3564177, 4857631, 6572314, 8884973, 11930363, 16002853
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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) = 14 split partitions:
(4)
(31)
(22)
(211)
(3)(1)
(2)(2)
(1111)
(21)(1)
(2)(11)
(111)(1)
(11)(11)
(2)(1)(1)
(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], OrderedQ[Total/@#, GreaterEqual]&]], {y, IntegerPartitions[n]}], {n, 10}]
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PROG
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(PARI) a(n)={my(recurse(r, m, s, t, f)=if(m==0, r==0, if(f, self()(r, min(m, t), t, 0, 0)) + self()(r, m-1, s, t, 0) + if(t+m<=s, self()(r-m, min(m, r-m), s, t+m, 1)))); recurse(n, n, n, 0, 0)} \\ Andrew Howroyd, Jan 18 2024
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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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