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A306901 Sum over all partitions of n of the bitwise AND of the parts. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A046974 A177986 A186775

Adjacent sequences:  A306898 A306899 A306900 * A306902 A306903 A306904

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Mar 15 2019

STATUS

approved

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Last modified January 23 01:48 EST 2020. Contains 331166 sequences. (Running on oeis4.)