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A306902 Sum over all partitions of n of the bitwise OR of the parts. 6


%S 0,1,3,7,13,23,40,67,103,156,231,340,486,689,964,1352,1845,2507,3363,

%T 4500,5937,7814,10174,13247,17064,21930,27957,35616,45009,56805,71252,

%U 89320,111282,138479,171421,212021,260974,320837,392753,480395,585239,712163,863536

%N Sum over all partitions of n of the bitwise OR of the parts.

%H Alois P. Heinz, <a href="/A306902/b306902.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<1, 0, (t->

%p `if`(i<n, b(n-i, min(i, 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..45);

%Y Cf. A006906, A066186, A306884, A306895, A306901, A306903, A306924.

%K nonn,base

%O 0,3

%A _Alois P. Heinz_, Mar 15 2019

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)