OFFSET
0,3
COMMENTS
We define the half-alternating sum of a sequence (A, B, C, D, E, F, G, ...) to be A + B - C - D + E + F - G - ...
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..250 (first 51 terms from Lucas A. Brown)
Lucas A. Brown, A357639.py.
EXAMPLE
The a(0) = 1 through a(6) = 15 reversed partitions:
() . (112) (123) (134) (145) (156)
(1111) (224) (235) (246)
(2222) (11233) (336)
(11222) (1111123) (3333)
(1111112) (11244)
(11111111) (11334)
(12333)
(1111134)
(1111224)
(1112223)
(1122222)
(11112222)
(111111222)
(11111111112)
(111111111111)
MATHEMATICA
halfats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[i/2]), {i, Length[f]}];
Table[Length[Select[IntegerPartitions[2n], halfats[Reverse[#]]==0&]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 11 2022
EXTENSIONS
a(31) onwards from Lucas A. Brown, Oct 19 2022
STATUS
approved