A176368 x-values in the solution to x^2 - 65*y^2 = 1.

1, 129, 33281, 8586369, 2215249921, 571525893249, 147451465208321, 38041906497853569, 9814664424981012481, 2532145379738603366529, 653283693308134687552001, 168544660728119010785049729

Offset: 1

Author

Vincenzo Librandi, Apr 16 2010

Keywords

• nonn
• easy

Comments

The corresponding values of y of this Pell equation are in A176369.

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. A176369, Row 8 of array A188645.

Programs

GAP

a:=[1,129];; 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:=[1, 129]; [n le 2 select I[n] else 258*Self(n-1)-Self(n-2): n in [1..20]];

Maple

seq(coeff(series(x*(1-129*x)/(1-258*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{258,-1},{1,129},30]

PARI

my(x='x+O('x^15)); Vec(x*(1-129*x)/(1-258*x+x^2)) \\ G. C. Greubel, Dec 08 2019

Sage

def A176368_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1-129*x)/(1-258*x+x^2) ).list()
a=A176368_list(15); a[1:] # G. C. Greubel, Dec 08 2019

Formula

a(n) = 258*a(n-1) - a(n-2) with a(1)=1, a(2)=129.

G.f.: x*(1-129*x)/(1-258*x+x^2).