A307435 Number of partitions of n into parts whose bitwise AND equals 0.

1, 0, 0, 1, 1, 3, 5, 9, 11, 18, 27, 38, 53, 75, 102, 137, 178, 238, 313, 406, 528, 677, 865, 1093, 1382, 1742, 2181, 2717, 3377, 4175, 5146, 6320, 7737, 9454, 11516, 13986, 16950, 20473, 24682, 29672, 35631, 42663, 50992, 60807, 72399, 86008, 102027, 120793

Offset: 0

Author

Alois P. Heinz, Apr 08 2019

Keywords

• nonn
• base

Examples

			a(0) = 1: the empty partition.
a(3) = 1: 21.
a(4) = 1: 211.
a(5) = 3: 2111, 221, 41.
a(6) = 5: 21111, 2211, 321, 411, 42.
a(7) = 9: 211111, 22111, 2221, 3211, 4111, 421, 43, 52, 61.
a(8) = 11: 2111111, 221111, 22211, 32111, 3221, 41111, 4211, 422, 431, 521, 611.
a(9) = 18: 21111111, 2211111, 222111, 22221, 321111, 32211, 3321, 411111, 42111, 4221, 4311, 432, 441, 5211, 522, 6111, 621, 81.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1024
• Wikipedia, Bitwise operation
• Wikipedia, Partition (number theory)

Crossrefs

Column k=0 of A307432.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0),
     `if`(i<1, 0, b(n, i-1, k)+b(n-i, min(n-i, i), Bits[And](i, k))))
    end:
a:= n-> b(n$2, `if`(n=0, 0, 2^ilog2(2*n)-1)):
seq(a(n), n=0..50);