A121655 A trisection of A121653; a(n) = A121653(3*n+1) = A121652(3*n+1)^(1/3).

1, 2, 6, 19, 67, 243, 895, 3366, 12687, 47893, 181457, 687963, 2608418, 9980210, 38267955, 146847036, 566931450, 2192350203, 8483412214, 32931060365, 127961086743, 497417231082, 1939118056782, 7565621219100, 29525286454134

Offset

0,2

Links

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

Formula

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

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 19*x^3 + 67*x^4 + 243*x^5 + 895*x^6 +...
B(x)/A(x) = 1 - x - 3*x^2 - 6*x^3 - 10*x^4 - 36*x^5 - 141*x^6 -...
B(x)/A(x) = 1 - x*B(x)^3, where
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+1))}

Crossrefs

Cf. A121652, A121653; A121654, A121656.

Sequence in context: A305118 A234010 A360212 * A250918 A150095 A150096

Adjacent sequences: A121652 A121653 A121654 * A121656 A121657 A121658

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved