OFFSET
0,2
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
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 11 2005
STATUS
approved