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A218031 G.f. A(x) satisfies A(x) = 1 + x / A(x^2). 3
1, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 3, 0, -1, 0, -3, 0, 6, 0, -4, 0, -4, 0, 12, 0, -10, 0, -5, 0, 23, 0, -25, 0, -2, 0, 43, 0, -57, 0, 12, 0, 74, 0, -124, 0, 56, 0, 120, 0, -258, 0, 172, 0, 170, 0, -516, 0, 454, 0, 187, 0, -989, 0, 1095, 0, 40, 0, -1811, 0, 2487 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Cf. A101912, A238429.

Sequence in context: A243016 A284975 A219202 * A135523 A194663 A135685

Adjacent sequences:  A218028 A218029 A218030 * A218032 A218033 A218034

KEYWORD

sign,changed

AUTHOR

Joerg Arndt, Oct 18 2012

STATUS

approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)