|
|
A366527
|
|
Number of integer partitions of 2n containing at least one even part.
|
|
3
|
|
|
0, 1, 3, 7, 16, 32, 62, 113, 199, 339, 563, 913, 1453, 2271, 3496, 5308, 7959, 11798, 17309, 25151, 36225, 51748, 73359, 103254, 144363, 200568, 277007, 380437, 519715, 706412, 955587, 1286762, 1725186, 2303388, 3063159, 4058041, 5356431, 7045454, 9235841
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Also partitions of 2n with even product.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(1) = 1 through a(4) = 16 partitions:
(2) (4) (6) (8)
(22) (42) (44)
(211) (222) (62)
(321) (332)
(411) (422)
(2211) (431)
(21111) (521)
(611)
(2222)
(3221)
(4211)
(22211)
(32111)
(41111)
(221111)
(2111111)
|
|
MATHEMATICA
|
Table[Length[Select[IntegerPartitions[2n], Or@@EvenQ/@#&]], {n, 0, 15}]
|
|
CROSSREFS
|
This is the even bisection of A047967.
A006477 counts partitions w/ at least one odd and even part, ranks A366532.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|