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%I #13 Mar 19 2019 04:32:39
%S 0,1,2,6,7,13,20,35,42,58,75,104,133,176,233,327,402,500,616,762,916,
%T 1112,1329,1640,1967,2350,2787,3352,3960,4706,5571,6706,7922,9374,
%U 10982,12933,15090,17578,20322,23692,27391,31626,36308,41788,47799,54704,62258
%N Sum over all partitions of n into distinct parts of the bitwise OR of the parts.
%H Alois P. Heinz, <a href="/A306924/b306924.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Commutative_property">Commutative property</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Identity_element">Identity element</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truth_table">Truth table</a>
%p b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n or
%p n=0, 0, (t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)
%p +`if`(i=n, t, 0)+b(n, i-1, r))(Bits[Or](i, r)))
%p end:
%p a:= n-> b(n$2, 0):
%p seq(a(n), n=0..49);
%Y Cf. A000009, A066189, A306902, A306923, A306925.
%K nonn,base
%O 0,3
%A _Alois P. Heinz_, Mar 16 2019
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