A165443 a(n) = ( 16^(2*n+1) + 81^(2*n+1) )/97.

1, 5521, 35957041, 235845988561, 1547368082644081, 10152277523461827601, 66609091687940958003121, 437022250271846649679394641, 2867302983958645970747063186161, 18812374877733491600234823630721681

Offset: 0

Author

Jaume Oliver Lafont, Sep 19 2009

Keywords

• nonn
• easy

Comments

The general form of the g.f. for (A^(2*n+1)+B^(2*n+1))/(A+B) is (1-A*B*x)/((1-A^2*x)(1-B^2*x)).

Examples

			a(0) = (16^1 + 81^1)/97 = 97/97 = 1.
a(1) = (16^3 + 81^3)/97 = 535537/97 = 5521.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..260
• Index entries for linear recurrences with constant coefficients, signature (6817,-1679616).

Crossrefs

Cf. A007689, A082101, A096951, A165259.

Programs

GAP

List([0..10],n->(16^(2*n+1)+81^(2*n+1))/97); # Muniru A Asiru, Oct 21 2018

Magma

[(2^(8*n+4) + 3^(8*n+4))/97: n in [0..20]]; // G. C. Greubel, Oct 20 2018

Maple

seq(coeff(series((1-16*81*x)/((1-16^2*x)*(1-81^2*x)),x,n+1), x, n), n = 0 .. 10); # Muniru A Asiru, Oct 21 2018

Mathematica

f[n_]:=Module[{c=2n+1},(16^c+81^c)/97]; Array[f,20,0] (* Harvey P. Dale, Oct 02 2012 *)

PARI

a(n)=(16^(2*n+1)+81^(2*n+1))/97

Python

for n in range(0, 10): print(int((16**(2*n+1)+81**(2*n+1))/97), end=', ') # Stefano Spezia, Oct 21 2018

Formula

G.f.: (1 - 16*81*x)/((1 - 16^2*x)*(1 - 81^2*x)).

a(n) = (16^2+81^2)*a(n-1) - 16^2*81^2*a(n-2).

Extensions

Definition replaced with formula by R. J. Mathar, Sep 21 2009