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A307506 Number of partitions of 2n into distinct parts whose bitwise XOR equals 0.

%I A307506 #11 Apr 12 2019 08:59:27
%S A307506 1,0,0,1,0,1,1,8,1,2,1,9,2,9,10,80,38,39,39,47,40,48,91,126,85,86,136,
%T A307506 165,174,244,512,1187,1117,1135,1741,1374,1932,1990,4284,2665,3200,
%U A307506 2832,5566,3904,6182,6676,15426,11394,12304,11223,15799,12630,15956,17969
%N A307506 Number of partitions of 2n into distinct parts whose bitwise XOR equals 0.
%C A307506 There are no partitions of 2n+1 into distinct parts whose bitwise XOR equals 0.
%H A307506 Alois P. Heinz, <a href="/A307506/b307506.txt">Table of n, a(n) for n = 0..750</a>
%H A307506 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H A307506 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%F A307506 a(n) = A307505(2n,0).
%p A307506 b:= proc(n, i, k) option remember; `if`(i*(i+2)/2<n, 0,
%p A307506       `if`(n=0, `if`(k=0, 1, 0), b(n, i-1, k)+
%p A307506        b(n-i, min(n-i, i-1), Bits[Xor](i, k))))
%p A307506     end:
%p A307506 a:= n-> b(2*n$2, 0):
%p A307506 seq(a(n), n=0..60);
%Y A307506 Bisection (even part) of column k=0 of A307505.
%K A307506 nonn,base
%O A307506 0,8
%A A307506 _Alois P. Heinz_, Apr 11 2019