OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f. satisfies: A(x) = 1+2*x - 2*x*(3+x)*A(x) + x*(4+3*x)*A(x)^2.
G.f.: A(x) = ( 1 +6*x +2*x^2 - sqrt(1 -4*x -4*x^2 +4*x^4) )/( 2*x*(4+3*x) ).
MATHEMATICA
f[x_]:= Sqrt[1-4*x-4*x^2+4*x^4];
CoefficientList[Series[(1+6*x+2*x^2-f[x])/(2*x*(4+3*x)), {x, 0, 30}], x] (* G. C. Greubel, Mar 17 2021 *)
PROG
(PARI) {a(n)=polcoeff(2*(1+2*x)/(1+6*x+2*x^2+sqrt(1-4*x-4*x^2+4*x^4+x*O(x^n))), n)}
(Sage)
def f(x): return sqrt(1-4*x-4*x^2+4*x^4)
def A122447_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( ( 1+6*x+2*x^2 -f(x) )/( 2*x*(4+3*x) ) ).list()
A122447_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!( ( 1+6*x+2*x^2 -f(x) )/( 2*x*(4+3*x) ) )); // G. C. Greubel, Mar 17 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 07 2006
STATUS
approved