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

0,8

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)

Formula

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

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+2)/2<n, 0,
      `if`(n=0, `if`(k=0, 1, 0), b(n, i-1, k)+
       b(n-i, min(n-i, i-1), Bits[Xor](i, k))))
    end:
a:= n-> b(2*n$2, 0):
seq(a(n), n=0..60);

Crossrefs

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

Sequence in context: A109011 A225767 A019763 * A179050 A176458 A355708

Adjacent sequences: A307503 A307504 A307505 * A307507 A307508 A307509

Keyword

nonn,base

Author

Alois P. Heinz, Apr 11 2019

Status

approved