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.

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

Links

Table of n, a(n) for n=1..60.

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.

Cf. A001055, A051293, A067538, A102627, A326028, A326622, A326647, A326666, A326667.

Sequence in context: A338903 A362830 A248519 * A361178 A307993 A114092

Adjacent sequences: A326667 A326668 A326669 * A326671 A326672 A326673

Keyword

nonn

Author

Gus Wiseman, Jul 17 2019

Status

approved