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 A318684 Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..49. EXAMPLE 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) 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/@#, Greater]&]], {y, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}] CROSSREFS Cf. A001970, A063834, A316245, A317508, A317546, A317715, A318434, A318683, A319794. Sequence in context: A079965 A285069 A262736 * A336132 A200737 A200741 Adjacent sequences: A318681 A318682 A318683 * A318685 A318686 A318687 KEYWORD nonn AUTHOR Gus Wiseman, Sep 29 2018 STATUS approved

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Last modified June 2 14:40 EDT 2023. Contains 363097 sequences. (Running on oeis4.)