OFFSET
0,3
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(1) = 1 through a(7) = 12 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (41) (33) (61)
(111) (31) (221) (42) (322)
(211) (311) (51) (331)
(1111) (2111) (222) (421)
(11111) (411) (511)
(2211) (2221)
(3111) (4111)
(21111) (22111)
(111111) (31111)
(211111)
(1111111)
MATHEMATICA
altprod[q_]:=Product[q[[i]]^(-1)^(i-1), {i, Length[q]}];
Table[Length[Select[IntegerPartitions[n], IntegerQ[altprod[#]]&]], {n, 0, 30}]
CROSSREFS
Allowing any reverse-alternating product >= 1 gives A344607.
Allowing any reverse-alternating product < 1 gives A344608.
Ranked by A347457.
The even-length case is A347704.
A000041 counts partitions.
A027187 counts partitions of even length.
A027193 counts partitions of odd length.
A347461 counts possible alternating products of partitions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2021
STATUS
approved