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

0,3

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<1, 0, (t->
      `if`(i<n, b(n-i, min(i, 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..55);

Crossrefs

Cf. A006906, A066186, A306884, A306895, A306902, A306903, A306923.

Sequence in context: A219658 A047204 A050035 * A355477 A341578 A368641

Adjacent sequences: A306898 A306899 A306900 * A306902 A306903 A306904

Keyword

nonn,base

Author

Alois P. Heinz, Mar 15 2019

Status

approved