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

0,3

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

Formula

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

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

Maple

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n or
      n=0, 0, (t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)
      +`if`(i=n, t, 0)+b(n, i-1, r))(Bits[Xor](i, r)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..51);

Crossrefs

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

Sequence in context: A200809 A323444 A099027 * A134466 A062562 A208570

Adjacent sequences: A306922 A306923 A306924 * A306926 A306927 A306928

Keyword

nonn,base

Author

Alois P. Heinz, Mar 16 2019

Status

approved