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 A319794 Number of ways to split a strict integer partition of n into consecutive subsequences with weakly decreasing sums. 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS EXAMPLE The a(6) = 9 split partitions:     (6)    (51)  (5)(1)    (42)  (4)(2)   (321)  (32)(1)  (3)(21)  (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], OrderedQ[Total/@#, GreaterEqual]&]], {y, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}] CROSSREFS Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A318684. Sequence in context: A213933 A091916 A102437 * A072706 A117433 A159284 Adjacent sequences:  A319791 A319792 A319793 * A319795 A319796 A319797 KEYWORD nonn AUTHOR Gus Wiseman, Sep 29 2018 STATUS approved

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Last modified January 27 14:29 EST 2021. Contains 340467 sequences. (Running on oeis4.)