login
A319794
Number of ways to split a strict integer partition of n into consecutive subsequences with weakly decreasing sums.
17
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
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 29 2018
STATUS
approved