OFFSET
1,2
COMMENTS
Also the number of integer partitions y of n such that the average of the multiset {2^s: s in y} is an integer.
EXAMPLE
The a(1) = 1 through a(8) = 11 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (43) (44)
(111) (31) (41) (42) (52) (53)
(1111) (311) (51) (61) (62)
(11111) (222) (331) (71)
(2211) (511) (422)
(111111) (3211) (2222)
(1111111) (3311)
(4211)
(311111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[2^#]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved