OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A(x) = B(x)*(B(x)-1)/(x*(1+x -x*B(x))) where B(x) is the g.f. of A122446.
G.f.: 2*(1-2*x^2-f(x))/(x*(1+2*x^2+f(x))*(1-x+2*x^2+2*x^3+(1+x)*f(x))), where f(x) = sqrt(1 -4*x -4*x^2 +4*x^4). - G. C. Greubel, Mar 17 2021
MATHEMATICA
f[x_]:= Sqrt[1-4*x-4*x^2+4*x^4];
CoefficientList[Series[2*(1-2*x^2-f[x])/(x*(1+2*x^2+f[x])*(1-x+2*x^2+2*x^3+(1+x)*f[x])), {x, 0, 30}], x] (* G. C. Greubel, Mar 17 2021 *)
PROG
(PARI) {a(n)=local(A, B=2/(1+2*x^2+sqrt(1-4*x-4*x^2+4*x^4+x^2*O(x^n)))); A=B*(B-1)/x/(1+x-x*B); polcoeff(A, n, x)}
(Sage)
def f(x): return sqrt(1-4*x-4*x^2+4*x^4)
def A122449_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 2*(1-2*x^2-f(x))/(x*(1+2*x^2+f(x))*(1-x+2*x^2+2*x^3+(1+x)*f(x))) ).list()
A122449_list(30) # G. C. Greubel, Mar 17 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
f:= func< x | Sqrt(1-4*x-4*x^2+4*x^4) >;
Coefficients(R!( 2*(1-2*x^2-f(x))/(x*(1+2*x^2+f(x))*(1-x+2*x^2+2*x^3+(1+x)*f(x))) )); // G. C. Greubel, Mar 17 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 07 2006
STATUS
approved