A307506 Number of partitions of 2n into distinct parts whose bitwise XOR equals 0.

1, 0, 0, 1, 0, 1, 1, 8, 1, 2, 1, 9, 2, 9, 10, 80, 38, 39, 39, 47, 40, 48, 91, 126, 85, 86, 136, 165, 174, 244, 512, 1187, 1117, 1135, 1741, 1374, 1932, 1990, 4284, 2665, 3200, 2832, 5566, 3904, 6182, 6676, 15426, 11394, 12304, 11223, 15799, 12630, 15956, 17969

Offset: 0

Author

Alois P. Heinz, Apr 11 2019

Keywords

• nonn
• base

Comments

There are no partitions of 2n+1 into distinct parts whose bitwise XOR equals 0.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750
• Wikipedia, Bitwise operation
• Wikipedia, Partition (number theory)

Crossrefs

Bisection (even part) of column k=0 of A307505.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+2)/2 b(2*n$2, 0):
seq(a(n), n=0..60);

Formula

a(n) = A307505(2n,0).