OFFSET
1,12
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 a(n) partitions for n = 1, 12, 15, 21, 24, 26:
(1) (12) (15) (21) (24) (26)
(9,2,1) (11,3,1) (15,5,1) (17,6,1) (11,8,4,2,1)
(9,3,2,1) (16,3,2) (18,4,2) (12,6,5,2,1)
(11,7,2,1) (12,9,2,1) (13,5,4,3,1)
(12,5,3,1) (13,7,3,1)
(10,5,3,2,1) (14,5,4,1)
(15,4,3,2)
(10,8,3,2,1)
(11,6,4,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[Total[Accumulate[#]], Total[Accumulate[Reverse[#]]]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 10 2023
STATUS
approved