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

1, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 67, 102, 150, 243, 378, 568, 895, 1390, 2115, 3366, 5229, 7974, 12687, 19785, 30307, 47893, 74761, 115063, 181457, 283143, 436831, 687963, 1073820, 1659809, 2608418, 4072442, 6306619, 9980210, 15617469

Offset

0,5

Links

Table of n, a(n) for n=0..41.

Formula

a(n) = A121652(n)^(1/3).

Example

A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...
The coefficients of 1 - 1/A(x) equal the cube of each term:
1/A(x) = 1 - x - x^4 - x^7 - x^10 - 8*x^13 - 27*x^16 - 64*x^19 - 216*x^22 -... - a(n)^3*x^(3*n+1) -...

Prog

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

Crossrefs

Cf. A121652; trisections: A121654, A121655, A121656.

Sequence in context: A199804 A101913 A352042 * A375922 A238434 A061418

Adjacent sequences: A121650 A121651 A121652 * A121654 A121655 A121656

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved