A043699 a(n)= A000129(n)*A000129(2*n) where A000129(n) are the Pell numbers.

0, 2, 24, 350, 4896, 68962, 970200, 13652158, 192099456, 2703046850, 38034749784, 535189557278, 7530688519200, 105964828904482, 1491038292992664, 20980500931258750, 295218051329511936, 4154033219547089282, 58451683124982331800, 822477596969315258078

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (12,30,-12,-1).

Formula

a(n) is asymptotic to (1/8)*(7+2*sqrt(5))^n.

a(n) = 2 * A052208(n).

G.f.: 2*x*(x^2+1) / ((x^2-2*x-1)*(x^2+14*x-1)). - Colin Barker, Oct 19 2013

Prog

(PARI) a(n)=if(n<0, 0, contfracpnqn(vector(n, i, 1+(i>1)))[2, 1]*contfracpnqn(vector (2*n, i, 1+(i>1)))[2, 1])
(PARI) Vec(2*x*(x^2+1)/((x^2-2*x-1)*(x^2+14*x-1)) + O(x^100)) \\ Colin Barker, Oct 19 2013

Crossrefs

Cf. A000129.

Sequence in context: A333715 A081065 A262291 * A220317 A220340 A366003

Adjacent sequences: A043696 A043697 A043698 * A043700 A043701 A043702

Keyword

nonn,easy

Author

Gary W. Adamson, Feb 01 2000

Status

approved