A121656 - OEIS

%I #3 Mar 30 2012 18:36:58

%S 1,3,9,28,102,378,1390,5229,19785,74761,283143,1073820,4072442,

%T 15617469,59967564,230081349,889342557,3443431566,13326462430,

%U 51756384099,201245258853,782441280159,3052080395712,11914099660794,46498675915560

%N A trisection of A121653; a(n) = A121653(3*n+2) = A121652(3*n+2)^(1/3).

%F G.f.: A(x) = B(x)^2/(1 - x*B(x)^3), where B(x) = Sum_{n>=0} A121653(n)^3*x^n is the g.f. of A121652.

%e A(x) = 1 + 3*x + 9*x^2 + 28*x^3 + 102*x^4 + 378*x^5 + 1390*x^6 +...

%e B(x)^2/A(x) = 1 - x - 3*x^2 - 6*x^3 - 10*x^4 - 36*x^5 - 141*x^6 -...

%e B(x)^2/A(x) = 1 - x*B(x)^3, where

%e B(x)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + 19*x^4 + 72*x^5 + 199*x^6 +...

%e B(x)^3 = 1 + 3*x + 6*x^2 + 10*x^3 + 36*x^4 + 141*x^5 + 436*x^6 +...

%e and B(x) is g.f. of A121652 where all coefficients are cubes:

%e B(x) = 1 + x + x^2 + x^3 + 8*x^4 + 27*x^5 + 64*x^6 + 216*x^7 +...

%o (PARI) {a(n)=local(B=1+x);if(n==0, 1, for(m=0,n,B=1/(1-x*sum(k=0,m,polcoeff(B,k)^3*x^(3*k))+O(x^(3*n+3)))); polcoeff(B,3*n+2))}

%Y Cf. A121652, A121653; A121654, A121655.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 14 2006