A176372 y-values in the solution to x^2 - 66*y^2 = 1.

0, 8, 1040, 135192, 17573920, 2284474408, 296964099120, 38603048411192, 5018099329355840, 652314309767848008, 84795842170490885200, 11022807167854047227992, 1432880135978855648753760

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A176370.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (130,-1).

Formula

a(n) = 130*a(n-1) - a(n-2) with a(1)=0, a(2)=8.

G.f.: 8*x^2/(1-130*x+x^2).

Maple

seq(coeff(series(8*x^2/(1-130*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{130, -1}, {0, 8}, 30]

Prog

(Magma) I:=[0, 8]; [n le 2 select I[n] else 130*Self(n-1)-Self(n-2): n in [1..20]];
(PARI) my(x='x+O('x^15)); concat([0], Vec(8*x^2/(1-130*x+x^2))) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176372_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 8*x^2/(1-130*x+x^2) ).list()
a=A176372_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[0, 8];; for n in [3..15] do a[n]:=130*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 08 2019

Crossrefs

Cf. A176370.

Sequence in context: A004808 A320981 A316395 * A047943 A089672 A279881

Adjacent sequences: A176369 A176370 A176371 * A176373 A176374 A176375

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 16 2010

Extensions

Offset corrected by R. J. Mathar, Jun 18 2010

Status

approved