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A306923 Sum over all partitions of n into distinct parts of the bitwise AND of the parts.

%I A306923 #13 Mar 19 2019 04:33:17
%S A306923 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,
%T A306923 110,106,122,114,129,136,158,197,237,256,287,311,337,367,403,424,453,
%U A306923 492,525,571,638,684,754,809,853,896,955,995,1075,1149,1226,1295,1412
%N A306923 Sum over all partitions of n into distinct parts of the bitwise AND of the parts.
%H A306923 Alois P. Heinz, <a href="/A306923/b306923.txt">Table of n, a(n) for n = 0..1000</a>
%H A306923 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H A306923 Wikipedia, <a href="https://en.wikipedia.org/wiki/Commutative_property">Commutative property</a>
%H A306923 Wikipedia, <a href="https://en.wikipedia.org/wiki/Identity_element">Identity element</a>
%H A306923 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%H A306923 Wikipedia, <a href="https://en.wikipedia.org/wiki/Truth_table">Truth table</a>
%p A306923 b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n or
%p A306923       n=0, 0, (t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)
%p A306923       +`if`(i=n, t, 0)+b(n, i-1, r))(Bits[And](i, r)))
%p A306923     end:
%p A306923 a:= n-> b(n$2, 2^ilog2(2*n)-1):
%p A306923 seq(a(n), n=0..57);
%Y A306923 Cf. A000009, A066189, A306901, A306924, A306925.
%K A306923 nonn,base
%O A306923 0,3
%A A306923 _Alois P. Heinz_, Mar 16 2019