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A165443 a(n) = ( 16^(2*n+1) + 81^(2*n+1) )/97. 1
1, 5521, 35957041, 235845988561, 1547368082644081, 10152277523461827601, 66609091687940958003121, 437022250271846649679394641, 2867302983958645970747063186161, 18812374877733491600234823630721681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..260

Index entries for linear recurrences with constant coefficients, signature (6817,-1679616).

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).

EXAMPLE

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

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

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 *)

PROG

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

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

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

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

CROSSREFS

Cf. A007689, A082101, A096951, A165259.

Sequence in context: A234561 A252511 A250876 * A025296 A025315 A097103

Adjacent sequences:  A165440 A165441 A165442 * A165444 A165445 A165446

KEYWORD

nonn,easy

AUTHOR

Jaume Oliver Lafont, Sep 19 2009

EXTENSIONS

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

STATUS

approved

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Last modified January 17 12:18 EST 2020. Contains 330958 sequences. (Running on oeis4.)