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A307435 Number of partitions of n into parts whose bitwise AND equals 0.

%I A307435 #12 Apr 08 2019 17:42:49
%S A307435 1,0,0,1,1,3,5,9,11,18,27,38,53,75,102,137,178,238,313,406,528,677,
%T A307435 865,1093,1382,1742,2181,2717,3377,4175,5146,6320,7737,9454,11516,
%U A307435 13986,16950,20473,24682,29672,35631,42663,50992,60807,72399,86008,102027,120793
%N A307435 Number of partitions of n into parts whose bitwise AND equals 0.
%H A307435 Alois P. Heinz, <a href="/A307435/b307435.txt">Table of n, a(n) for n = 0..1024</a>
%H A307435 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H A307435 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e A307435 a(0) = 1: the empty partition.
%e A307435 a(3) = 1: 21.
%e A307435 a(4) = 1: 211.
%e A307435 a(5) = 3: 2111, 221, 41.
%e A307435 a(6) = 5: 21111, 2211, 321, 411, 42.
%e A307435 a(7) = 9: 211111, 22111, 2221, 3211, 4111, 421, 43, 52, 61.
%e A307435 a(8) = 11: 2111111, 221111, 22211, 32111, 3221, 41111, 4211, 422, 431, 521, 611.
%e A307435 a(9) = 18: 21111111, 2211111, 222111, 22221, 321111, 32211, 3321, 411111, 42111, 4221, 4311, 432, 441, 5211, 522, 6111, 621, 81.
%p A307435 b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0),
%p A307435      `if`(i<1, 0, b(n, i-1, k)+b(n-i, min(n-i, i), Bits[And](i, k))))
%p A307435     end:
%p A307435 a:= n-> b(n$2, `if`(n=0, 0, 2^ilog2(2*n)-1)):
%p A307435 seq(a(n), n=0..50);
%Y A307435 Column k=0 of A307432.
%K A307435 nonn,base
%O A307435 0,6
%A A307435 _Alois P. Heinz_, Apr 08 2019