A121651 A bisection of A121649; a(n) = A121649(2*n+1) = A121648(2*n+1)^(1/2).

1, 2, 5, 16, 51, 170, 564, 1972, 6847, 24340, 86071, 309554, 1108068, 4003278, 14415482, 52545636, 190858943, 698449146, 2548778173, 9373091678, 34371148421, 126710479728, 466022254144, 1723632401438, 6360225558484

Offset

0,2

Links

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

Formula

G.f.: A(x) = B(x)/(1 - x*B(x)^2), where B(x) = Sum_{n>=0} A121649(n)^2*x^n is the g.f. of A121648.

Example

A(x) = 1 + 2*x + 5*x^2 + 16*x^3 + 51*x^4 + 170*x^5 + 564*x^6 +...
B(x)/A(x) = 1 - x - 2*x^2 - 3*x^3 - 10*x^4 -27*x^5 -76*x^6 -212*x^7-...
B(x)/A(x) = 1 - x*B(x)^2, where
B(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 27*x^4 + 76*x^5 + 212*x^6 +...
and B(x) is the g.f. of A121648 where all coefficients are squares:
B(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 64*x^6 + 256*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)^2*x^(2*k))+O(x^(2*n+2)))); polcoeff(B, 2*n+1))}

Crossrefs

Cf. A121648, A121649, A121650.

Sequence in context: A118973 A148386 A148387 * A054660 A231296 A148388

Adjacent sequences: A121648 A121649 A121650 * A121652 A121653 A121654

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved