A107087 G.f. A(x) satisfies: A(x)^2 = A(x^2) + 4*x.

1, 2, -1, 2, -5, 12, -30, 82, -233, 668, -1949, 5802, -17503, 53302, -163783, 507418, -1582869, 4966790, -15667573, 49658264, -158059506, 505013014, -1619144976, 5207596574, -16797286048, 54323516786, -176113786590, 572236347200, -1863213388504, 6078422747600, -19865661574555

Offset

0,2

Comments

Self-convolution of A107086. Self-convolution yields A107088.

Links

Table of n, a(n) for n=0..30.

Formula

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w) = u^4 + 4*w - 2*u^2*v - 3*v^2. - Michael Somos, May 15 2005

Example

A(x)^2 = 1 + 4*x + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...
A(x^2) = 1 + 2*x^2 - x^4 + 2*x^6 - 5*x^8 + 12*x^10 - 30*x^12 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2)+4*x+x*O(x^n))^(1/2)); polcoeff(A, n, x)}
(PARI) {a(n)=local(m, A); if(n<0, 0, A=1+O(x); m=1; while(m<=n, A=sqrt(4*x+subst(A, x, x^2)); m*=2); polcoeff(A, n))} /* Michael Somos, May 15 2005 */

Crossrefs

Cf. A107086, A107088.

Sequence in context: A330962 A327194 A160457 * A279955 A280339 A115141

Adjacent sequences: A107084 A107085 A107086 * A107088 A107089 A107090

Keyword

sign

Author

Paul D. Hanna, May 11 2005

Status

approved