A306901 Sum over all partitions of n of the bitwise AND of the parts.

0, 1, 3, 4, 8, 9, 14, 13, 24, 28, 36, 38, 55, 54, 68, 75, 106, 120, 154, 168, 208, 228, 269, 298, 374, 404, 475, 530, 618, 682, 808, 896, 1080, 1220, 1410, 1581, 1828, 2022, 2322, 2598, 2963, 3278, 3732, 4128, 4684, 5218, 5888, 6550, 7418, 8192, 9198, 10187

Offset: 0

Author

Alois P. Heinz, Mar 15 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. A006906, A066186, A306884, A306895, A306902, A306903, A306923.

Programs

Maple

b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
      `if`(i b(n$2, 2^ilog2(2*n)-1):
seq(a(n), n=0..55);