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A318619 a(0) = 0, a(1) = 1; for n > 1, a(n) = Sum_{k=0..n-2} a(k) XOR a(n-k-2).

%I A318619 #9 Feb 16 2025 08:33:56
%S A318619 0,1,0,2,0,6,6,18,26,66,110,242,450,922,1826,3674,7290,14586,29178,
%T A318619 58410,116538,233258,466114,932426,1864586,3729274,7457386,14915578,
%U A318619 29828762,59659322,119313866,238631866,477253498,954516442,1909012410,3818036378,7636034202
%N A318619 a(0) = 0, a(1) = 1; for n > 1, a(n) = Sum_{k=0..n-2} a(k) XOR a(n-k-2).
%H A318619 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A318619 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/XOR.html">XOR</a>
%F A318619 a(n) ~ c * 2^n, where c = 0.111118791917413048987034558666...
%p A318619 a:= proc(n) option remember; `if`(n<2, n,
%p A318619       add(Bits[Xor](a(k), a(n-k-2)), k=0..n-2))
%p A318619     end:
%p A318619 seq(a(n), n=0..40); # _Alois P. Heinz_, Aug 30 2018
%t A318619 a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[BitXor[a[k], a[n - k - 2]], {k, 0, n - 2}]; Table[a[n], {n, 0, 36}]
%Y A318619 Cf. A007462, A192484.
%K A318619 nonn
%O A318619 0,4
%A A318619 _Ilya Gutkovskiy_, Aug 30 2018