A319794 Number of ways to split a strict integer partition of n into consecutive subsequences with weakly decreasing sums.

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

Offset

0,4

Links

Table of n, a(n) for n=0..49.

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 A349054

Adjacent sequences: A319791 A319792 A319793 * A319795 A319796 A319797

Keyword

nonn

Author

Gus Wiseman, Sep 29 2018

Status

approved