A176369 y-values in the solution to x^2 - 65*y^2 = 1.

0, 16, 4128, 1065008, 274767936, 70889062480, 18289103351904, 4718517775728752, 1217359297034666112, 314073980117168128144, 81029869510932342395040, 20905392259840427169792176

Offset: 1

Author

Vincenzo Librandi, Apr 16 2010

Keywords

• nonn
• easy

Comments

The corresponding values of x of this Pell equation are in A176368.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (258,-1).

Crossrefs

Cf. A176368.

Programs

GAP

a:=[1,16];; for n in [3..15] do a[n]:=258*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 08 2019

Magma

I:=[0,16]; [n le 2 select I[n] else 258*Self(n-1)-Self(n-2): n in [1..20]];

Maple

seq(coeff(series(16*x^2/(1-258*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{258,-1},{0,16},20] (* Harvey P. Dale, Aug 20 2011 *)

PARI

my(x='x+O('x^15)); concat([0], Vec(16*x^2/(1-258*x+x^2))) \\ G. C. Greubel, Dec 08 2019

Sage

def A176369_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 16*x^2/(1-258*x+x^2) ).list()
a=A176369_list(15); a[1:] # G. C. Greubel, Dec 08 2019

Formula

a(n) = 258*a(n-1) - a(n-2) with a(0)=0, a(1)=16.

G.f.: 16*x^2/(1-258*x+x^2).

Extensions

Partially corrected and edited by Michael B. Porter and N. J. A. Sloane, Jun 22 2010