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A068012 Number of subsets of {1,2,3,...,n} that sum to 0 mod 6.

%I A068012 #16 Sep 04 2025 10:52:30
%S A068012 1,1,1,2,3,6,12,22,44,88,172,344,688,1368,2736,5472,10928,21856,43712,
%T A068012 87392,174784,349568,699072,1398144,2796288,5592448,11184896,22369792,
%U A068012 44739328,89478656,178957312,357914112,715828224,1431656448,2863311872,5726623744
%N A068012 Number of subsets of {1,2,3,...,n} that sum to 0 mod 6.
%F A068012 Empirical g.f.: (x-1)*(2*x^4+3*x^3+x^2-1) / ((2*x-1)*(2*x^3-1)). - _Colin Barker_, Dec 22 2012
%p A068012 b:= proc(n, s) option remember; `if`(n=0, `if`(s=0, 1, 0),
%p A068012       b(n-1, s)+b(n-1, irem(s+n, 6)))
%p A068012     end:
%p A068012 a:= n-> b(n, 0):
%p A068012 seq(a(n), n=0..35);  # _Alois P. Heinz_, May 02 2025
%t A068012 b[n_, s_] := b[n, s] = If[n == 0, If[s == 0, 1, 0], b[n-1, s] + b[n-1, Mod[s+n, 6]]];
%t A068012 a[n_] := b[n, 0];
%t A068012 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Sep 04 2025, after _Alois P. Heinz_ *)
%Y A068012 6th row of A068009.
%K A068012 nonn,changed
%O A068012 0,4
%A A068012 _Antti Karttunen_, Feb 11 2002