login
A317715
Number of ways to split an integer partition of n into consecutive subsequences with equal sums.
22
1, 1, 3, 4, 9, 8, 21, 16, 39, 38, 64, 57, 146, 102, 186, 211, 352, 298, 593, 491, 906, 880, 1273, 1256, 2444, 1998, 3038, 3277, 4861, 4566, 7710, 6843, 10841, 10742, 14966, 15071, 24499, 21638, 31334, 32706, 47157, 44584, 67464, 63262, 91351, 94247, 125248
OFFSET
0,3
EXAMPLE
The a(4) = 9 constant-sum split partitions:
(4),
(31),
(22), (2)(2),
(211), (2)(11),
(1111), (11)(11), (1)(1)(1)(1).
The a(6) = 21 constant-sum split partitions:
(6),
(51),
(42),
(411),
(33), (3)(3),
(321), (3)(21),
(3111), (3)(111),
(222), (2)(2)(2),
(2211), (2)(2)(11),
(21111), (21)(111), (2)(11)(11),
(111111), (111)(111), (11)(11)(11), (1)(1)(1)(1)(1)(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], SameQ@@Total/@#&]], {y, IntegerPartitions[n]}], {n, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 29 2018
EXTENSIONS
a(16)-a(46) from Hiroaki Yamanouchi, Oct 02 2018
STATUS
approved