A318684 Number of ways to split a strict integer partition of n into consecutive subsequences with strictly decreasing sums.

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

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