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A307506 Number of partitions of 2n into distinct parts whose bitwise XOR equals 0. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A222217

Adjacent sequences:  A307503 A307504 A307505 * A307507 A307508 A307509

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Apr 11 2019

STATUS

approved

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Last modified May 31 00:29 EDT 2020. Contains 334747 sequences. (Running on oeis4.)