A121656 A trisection of A121653; a(n) = A121653(3*n+2) = A121652(3*n+2)^(1/3).

1, 3, 9, 28, 102, 378, 1390, 5229, 19785, 74761, 283143, 1073820, 4072442, 15617469, 59967564, 230081349, 889342557, 3443431566, 13326462430, 51756384099, 201245258853, 782441280159, 3052080395712, 11914099660794, 46498675915560

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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.

Example

A(x) = 1 + 3*x + 9*x^2 + 28*x^3 + 102*x^4 + 378*x^5 + 1390*x^6 +...
B(x)^2/A(x) = 1 - x - 3*x^2 - 6*x^3 - 10*x^4 - 36*x^5 - 141*x^6 -...
B(x)^2/A(x) = 1 - x*B(x)^3, where
B(x)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + 19*x^4 + 72*x^5 + 199*x^6 +...
B(x)^3 = 1 + 3*x + 6*x^2 + 10*x^3 + 36*x^4 + 141*x^5 + 436*x^6 +...
and B(x) is g.f. of A121652 where all coefficients are cubes:
B(x) = 1 + x + x^2 + x^3 + 8*x^4 + 27*x^5 + 64*x^6 + 216*x^7 +...

Prog

(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))}

Crossrefs

Cf. A121652, A121653; A121654, A121655.

Sequence in context: A148934 A148935 A148936 * A148937 A047137 A058145

Adjacent sequences: A121653 A121654 A121655 * A121657 A121658 A121659

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved