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A318684 Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums. 6
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 * A200737 A200741 A271970

Adjacent sequences:  A318681 A318682 A318683 * A318685 A318686 A318687

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 29 2018

STATUS

approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)