A306923 Sum over all partitions of n into distinct parts of the bitwise AND of the parts.

0, 1, 2, 3, 5, 7, 7, 7, 12, 18, 18, 22, 23, 25, 19, 26, 37, 49, 55, 64, 67, 78, 80, 93, 101, 110, 106, 122, 114, 129, 136, 158, 197, 237, 256, 287, 311, 337, 367, 403, 424, 453, 492, 525, 571, 638, 684, 754, 809, 853, 896, 955, 995, 1075, 1149, 1226, 1295, 1412

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

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[And](i, r)))
    end:
a:= n-> b(n$2, 2^ilog2(2*n)-1):
seq(a(n), n=0..57);

Crossrefs

Cf. A000009, A066189, A306901, A306924, A306925.

Sequence in context: A353955 A318954 A296375 * A366856 A137750 A196365

Adjacent sequences: A306920 A306921 A306922 * A306924 A306925 A306926

Keyword

nonn,base

Author

Alois P. Heinz, Mar 16 2019

Status

approved