OFFSET
0,9
COMMENTS
The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i. The alternating sum of a partition is also the number of odd conjugate parts.
EXAMPLE
The a(1) = 0 through a(12) = 6 partitions:
. . 21 . 32 3111 43 3221 54 3331 65 4332
4211 411111 4222 422111 4431
4321 521111 5322
5311 5421
6411
51111111
MATHEMATICA
ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}];
Table[Length[Select[IntegerPartitions[n], Length[#]==2ats[#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 16 2022
STATUS
approved