OFFSET
1,3
COMMENTS
Also the number of strict integer partitions y of n such that the average of the set {2^s: s in y} is an integer.
EXAMPLE
The a(1) = 1 through a(11) = 7 partitions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(21) (31) (32) (42) (43) (53) (54) (64) (65)
(41) (51) (52) (62) (63) (73) (74)
(61) (71) (72) (82) (83)
(81) (91) (92)
(531) (A1)
(731)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[2^#]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved