OFFSET
1,2
COMMENTS
The (one-based) weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i. This is also the sum of partial sums of the reverse.
EXAMPLE
The partition (6,5,4,3,2,1,1,1,1) has weighted sum 80, reverse 160, so is counted under a(24).
The a(n) partitions for n = 1, 2, 4, 6, 9, 12, 14 (A..E = 10-14):
1 2 4 6 9 C E
11 22 33 333 66 77
1111 222 711 444 65111
111111 6111 921 73211
111111111 3333 2222222
7311 71111111
63111 11111111111111
222222
621111
111111111111
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Divisible[Total[Accumulate[#]], Total[Accumulate[Reverse[#]]]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 10 2023
STATUS
approved