A121654 - OEIS

A121654

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

1, 1, 4, 13, 41, 150, 568, 2115, 7974, 30307, 115063, 436831, 1659809, 6306619, 24210855, 93152526, 357925365, 1384070472, 5365825156, 20791117843, 80784911668, 314369613909, 1223297887923, 4773716056341, 18647712778338

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OFFSET

0,3

LINKS

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

FORMULA

G.f.: A(x) = 1/(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 + x + 4*x^2 + 13*x^3 + 41*x^4 + 150*x^5 + 568*x^6 +...

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

1/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 +...

Notice that coefficients are related by A121652(n) = A121653(n)^3.

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))}

CROSSREFS

Cf. A121652, A121653; A121655, A121656.

Sequence in context: A001453 A005002 A085507 * A186202 A036366 A303863

Adjacent sequences: A121651 A121652 A121653 * A121655 A121656 A121657

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 14 2006

STATUS

approved