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

%I A306901 #15 Mar 19 2019 17:20:26
%S A306901 0,1,3,4,8,9,14,13,24,28,36,38,55,54,68,75,106,120,154,168,208,228,
%T A306901 269,298,374,404,475,530,618,682,808,896,1080,1220,1410,1581,1828,
%U A306901 2022,2322,2598,2963,3278,3732,4128,4684,5218,5888,6550,7418,8192,9198,10187
%N A306901 Sum over all partitions of n of the bitwise AND of the parts.
%H A306901 Alois P. Heinz, <a href="/A306901/b306901.txt">Table of n, a(n) for n = 0..1000</a>
%H A306901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H A306901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Commutative_property">Commutative property</a>
%H A306901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Identity_element">Identity element</a>
%H A306901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%H A306901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Truth_table">Truth table</a>
%p A306901 b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
%p A306901       `if`(i<n, b(n-i, min(i, n-i), t), 0)+
%p A306901       `if`(i=n, t, 0)+b(n, i-1, r))(Bits[And](i, r)))
%p A306901     end:
%p A306901 a:= n-> b(n$2, 2^ilog2(2*n)-1):
%p A306901 seq(a(n), n=0..55);
%Y A306901 Cf. A006906, A066186, A306884, A306895, A306902, A306903, A306923.
%K A306901 nonn,base
%O A306901 0,3
%A A306901 _Alois P. Heinz_, Mar 15 2019