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}.

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, 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, 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

Offset: 0

Author

Paul D. Hanna, Nov 14 2012

Keywords

• nonn

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A080100.

Programs

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))}

Formula

a(n) == A001764(n) (mod 3), where A001764(n) = binomial(3*n,n)/(2*n+1).

G.f.: A(x) == G(x) (mod 3), where G(x) = 1 +x*G(x)^3 is the g.f. of A001764.

Define trisections by: A(x) = A0(x^3) + x*A1(x^3) + x^2*A2(x^3), then

A0(x) = 3*A(x) - 2,

A1(x) = A(x),

A2(x^3) = (2+A(x) - (3+x)*A(x^3))/x^2.