OFFSET
1,4
COMMENTS
A partition of n is a weakly decreasing sequence of positive integers summing to n.
The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i.
FORMULA
a(n) = A357189(2n - 1).
EXAMPLE
The a(1) = 1 through a(7) = 9 partitions:
(1) . (311) (322) (333) (443) (553)
(421) (432) (542) (652)
(531) (641) (751)
(51111) (52211) (52222)
(62111) (53311)
(62221)
(63211)
(73111)
(7111111)
MATHEMATICA
ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}];
Table[Length[Select[IntegerPartitions[n], Length[#]==ats[#]&]], {n, 1, 30, 2}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 02 2022
EXTENSIONS
More terms from Alois P. Heinz, Oct 04 2022
STATUS
approved