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

1, 1, 1, 2, 3, 5, 8, 16, 27, 51, 89, 170, 300, 564, 1008, 1972, 3563, 6847, 12483, 24340, 44583, 86071, 158600, 309554, 572548, 1108068, 2057792, 4003278, 7451924, 14415482, 26913176, 52545636, 98321435, 190858943, 358017691, 698449146

Offset

0,4

Links

Table of n, a(n) for n=0..35.

Formula

a(n) = A121648(n)^(1/2).

G.f. satisfies: A(x)*A(-x) = ( A(x) + A(-x) )/2. - Paul D. Hanna, Aug 14 2006

Example

A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 16*x^7 + 27*x^8 +...
The coefficients of 1 - 1/A(x) equal the square of each term:
1/A(x) = 1 - x - x^3 - x^5 - 4*x^7 - 9*x^9 - 25*x^11 - 64*x^13 - 256*x^15 -... - a(n)^2*x^(2*n+1) -...

Prog

(PARI) {a(n)=local(B); if(n==0, 1, B=sum(k=0, n\2, a(k)^2*x^(2*k)); polcoeff(1/(1-x*B+x*O(x^n)), n))}
(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+x+O(x^2); while(m<=n, m*=2; A=1/(1-x*sum(k=0, m-1, polcoeff(A, k)^2*x^(2*k), O(x^(2*m))))); polcoeff(A, n))} /* Michael Somos, Aug 18 2006 */

Crossrefs

Cf. A121648; bisections: A121650, A121651.

Sequence in context: A215525 A192645 A050295 * A306622 A030034 A370002

Adjacent sequences: A121646 A121647 A121648 * A121650 A121651 A121652

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved