OFFSET
0,16
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
G.f. A(x) = 1/B(x) = 1 + x*B(x^2) where B(x) is the g.f. of A101912.
G.f.: 1+x/(1+x^2/(1+x^4/(1+x^8/(1+ ...)))) (continued fraction).
(A(x) + 1) / (A(x) - 1) = 1 + 2*A(x^2) / x. [Joerg Arndt, Feb 28 2014]
A(x^3) = F(x) - x where F(x) is the g.f. of A238429. [Joerg Arndt, Feb 28 2014]
MAPLE
P:= 1+x: d:= 1:
while d < 127 do
P:= convert(series(1+x/subs(x=x^2, P), x, 2+2*d), polynom);
d:= 1+2*d;
od:
seq(coeff(P, x, i), i=0..d); # Robert Israel, Mar 13 2018
MATHEMATICA
nmax = 75; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x] - (1 + x/A[x^2]) + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];
sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)
PROG
(PARI)
N=166; R=O('x^N); x='x+R;
A= 1; for (k=1, N+1, A = 1 + x / subst(A, 'x, 'x^2) + R; );
Vec(A)
CROSSREFS
KEYWORD
sign
AUTHOR
Joerg Arndt, Oct 18 2012
STATUS
approved