A121652 a(n) is the cube of the coefficient of x^n in 1/(1 - x*A(x^3)), where g.f. A(x) = Sum_{n>=0} a(n)*x^n.

1, 1, 1, 1, 8, 27, 64, 216, 729, 2197, 6859, 21952, 68921, 300763, 1061208, 3375000, 14348907, 54010152, 183250432, 716917375, 2685619000, 9460870875, 38136631896, 142973623989, 507024206424, 2042099126703, 7744763561625

Offset

0,5

Links

Table of n, a(n) for n=0..26.

Formula

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

Example

A(x) = 1 + x + x^2 + x^3 + 8*x^4 + 27*x^5 + 64*x^6 + 216*x^7 +...
Take the cube-root of each term, a(n)^(1/3) and
let B(x) be the g.f. of the resulting sequence:
B(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...
Then 1/B(x) = 1 - x*A(x^3):
1/B(x) = 1 - x - x^4 - x^7 - x^10 - 8*x^13 - 27*x^16 - 64*x^19 -...

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n\3, polcoeff(x^(n-3*k)*(sum(j=0, k, a(j)*x^(3*j))+x*O(x^n))^(n-3*k), n))^3)}

Crossrefs

Cf. A121653; trisections of A121653: A121654, A121655, A121656; variant: A121648.

Sequence in context: A179163 A050462 A112662 * A112989 A018832 A248705

Adjacent sequences: A121649 A121650 A121651 * A121653 A121654 A121655

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved