cp's OEIS Frontend

A219218 G.f. satisfies: A(x) = Sum_{n>=0} [A(x)^(2*n) (mod 3)]*x^n, where A(x)^(2*n) (mod 3) reduces all coefficients modulo 3 to {0,1,2}.

%I A219218 #12 Nov 17 2012 09:51:08
%S A219218 1,1,3,3,1,6,9,3,3,9,3,6,3,1,15,18,6,6,27,9,12,9,3,9,9,3,3,27,9,18,9,
%T A219218 3,18,18,6,6,9,3,6,3,1,42,45,15,15,54,18,24,18,6,18,18,6,6,81,27,36,
%U A219218 27,9,36,36,12,12,27,9,12,9,3,27,27,9,9,27,9,12,9,3,9,9,3,3,81,27,54
%N A219218 G.f. satisfies: A(x) = Sum_{n>=0} [A(x)^(2*n) (mod 3)]*x^n, where A(x)^(2*n) (mod 3) reduces all coefficients modulo 3 to {0,1,2}.
%H A219218 Paul D. Hanna, <a href="/A219218/b219218.txt">Table of n, a(n) for n = 0..500</a>
%F A219218 a(n) == A001764(n) (mod 3), where A001764(n) = binomial(3*n,n)/(2*n+1).
%F A219218 G.f.: A(x) == G(x) (mod 3), where G(x) = 1 +x*G(x)^3 is the g.f. of A001764.
%F A219218 Define trisections by: A(x) = A0(x^3) + x*A1(x^3) + x^2*A2(x^3), then
%F A219218 A0(x) = 3*A(x) - 2,
%F A219218 A1(x) = A(x),
%F A219218 A2(x^3) = (2+A(x) - (3+x)*A(x^3))/x^2.
%o A219218 (PARI) {A=1;for(i=1,122,A=Ser(sum(n=0,#A-1,Vec(1+x^n*A^(2*n) +x*O(x^#A))%3))-#A);Vec(A+O(x^122))}
%Y A219218 Cf. A080100.
%K A219218 nonn
%O A219218 0,3
%A A219218 _Paul D. Hanna_, Nov 14 2012