OFFSET
0,3
LINKS
R. P. Stanley, A Fibonacci lattice, Fib. Quart., 13 (1975), 215-232.
FORMULA
G.f.: G(z) = lim_{m->infinity} G_m(z), where G_m(z) = (2z^m)^(-1)*(1 - sqrt(1 - 4z^m * Sum_{k=0..m-1} z^k*G_k(z)^2)).
Given the AGM-like recursion f(a0,b0,c0) = (a1,b1,c1) where a0^2 = b0^2 + 2*a0*c0, a1^2 = b1^2 + 2*a1*c1, a1 = (a0 + b0)/2, c1=c0*x with initial values a0=1, c0=2*x, then the common limit of a and b is 1/A(x). - Michael Somos, Sep 18 2006
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=1+x*O(x^n); for(k=1, n, A=(1-sqrt(1-4*x*A))/2); polcoeff(A, 2*n))} /* Michael Somos, Sep 18 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, A=1+x*O(x^n); for(k=1, n, A*=2/(1+sqrt(1-A*4*x^k))); polcoeff(A, n))} /* Michael Somos, Sep 18 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Joerg Arndt, May 18 2014
STATUS
approved