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A326670
Number of strict integer partitions y of n such that the average of the set {2^(s - 1): s in y} is an integer.
4
1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 6, 6, 8, 7, 10, 9, 13, 12, 15, 16, 23, 22, 27, 31, 41, 41, 50, 57, 74, 75, 90, 99, 133, 127, 158, 167, 226, 203, 278, 262, 371, 325, 457, 387, 622, 484, 715, 606, 969, 672, 1178, 866, 1428, 1050, 1776, 1142, 2276, 1459, 2514, 1792
OFFSET
1,5
EXAMPLE
The a(1) = 1 through a(12) = 6 partitions (A = 10, B = 11, C = 12):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(32) (42) (43) (53) (54) (64) (65) (75)
(52) (62) (63) (73) (74) (84)
(72) (82) (83) (93)
(531) (92) (A2)
(731) (642)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[2^(#-1)]]&]], {n, 30}]
CROSSREFS
The non-strict case is A326671.
Strict factorizations with integer average are A326668.
Strict partitions with integer average are A102627.
Sequence in context: A338903 A362830 A248519 * A361178 A307993 A114092
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved