A306925 Sum over all partitions of n into distinct parts of the bitwise XOR of the parts.

0, 1, 2, 6, 6, 11, 16, 35, 36, 46, 50, 84, 94, 130, 158, 285, 338, 424, 460, 616, 672, 810, 816, 1162, 1346, 1680, 1754, 2308, 2562, 3164, 3288, 4486, 5306, 6838, 7522, 9627, 11006, 13496, 14200, 17462, 19682, 24036, 25650, 30842, 33884, 40302, 41644, 48896

Offset: 0

Author

Alois P. Heinz, Mar 16 2019

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Bitwise operation
• Wikipedia, Commutative property
• Wikipedia, Identity element
• Wikipedia, Partition (number theory)
• Wikipedia, Truth table

Crossrefs

Cf. A000009, A066189, A067588, A067589, A306903, A306923, A306924.

Programs

Maple

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2 `if`(i b(n$2, 0):
seq(a(n), n=0..51);

Formula

a(n) is odd <=> n in { A067589 }.

a(n) is odd <=> A067588(n) is odd.