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A306923 Sum over all partitions of n into distinct parts of the bitwise AND of the parts. 4
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 (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*(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: A160102 A318954 A296375 * A137750 A196365 A195882

Adjacent sequences:  A306920 A306921 A306922 * A306924 A306925 A306926

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Mar 16 2019

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)