OFFSET
0,5
COMMENTS
We define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)).
EXAMPLE
The a(2) = 1 through a(9) = 8 partitions:
(11) (21) (22) (41) (33) (61) (44) (63)
(31) (2111) (42) (2221) (62) (81)
(1111) (51) (4111) (71) (3321)
(2211) (211111) (2222) (4221)
(3111) (3221) (6111)
(111111) (3311) (222111)
(4211) (411111)
(5111) (21111111)
(221111)
(311111)
(11111111)
MATHEMATICA
altprod[q_]:=Product[q[[i]]^(-1)^(i-1), {i, Length[q]}];
Table[Length[Select[IntegerPartitions[n], EvenQ[Length[#]]&&IntegerQ[altprod[#]]&]], {n, 0, 30}]
CROSSREFS
The reverse and reciprocal versions are both A035363.
The odd-length instead of even-length version is A347444.
Allowing any length gives A347446.
A119620 counts partitions with alternating product 1.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2021
STATUS
approved