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A306902 Sum over all partitions of n of the bitwise OR of the parts.

%I A306902 #15 Mar 19 2019 17:20:03
%S A306902 0,1,3,7,13,23,40,67,103,156,231,340,486,689,964,1352,1845,2507,3363,
%T A306902 4500,5937,7814,10174,13247,17064,21930,27957,35616,45009,56805,71252,
%U A306902 89320,111282,138479,171421,212021,260974,320837,392753,480395,585239,712163,863536
%N A306902 Sum over all partitions of n of the bitwise OR of the parts.
%H A306902 Alois P. Heinz, <a href="/A306902/b306902.txt">Table of n, a(n) for n = 0..1000</a>
%H A306902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H A306902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Commutative_property">Commutative property</a>
%H A306902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Identity_element">Identity element</a>
%H A306902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%H A306902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Truth_table">Truth table</a>
%p A306902 b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->
%p A306902       `if`(i<n, b(n-i, min(i, n-i), t), 0)+
%p A306902       `if`(i=n, t, 0)+b(n, i-1, r))(Bits[Or](i, r)))
%p A306902     end:
%p A306902 a:= n-> b(n$2, 0):
%p A306902 seq(a(n), n=0..45);
%Y A306902 Cf. A006906, A066186, A306884, A306895, A306901, A306903, A306924.
%K A306902 nonn,base
%O A306902 0,3
%A A306902 _Alois P. Heinz_, Mar 15 2019