A176370 x-values in the solution to x^2 - 66*y^2 = 1.

1, 65, 8449, 1098305, 142771201, 18559157825, 2412547746049, 313612647828545, 40767231669964801, 5299426504447595585, 688884678346517461249, 89549708758542822366785, 11640773253932220390220801

Offset

1,2

Comments

The corresponding values of y of this Pell equation are in A176372.

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)=1, a(2)=65.

G.f.: x*(1-65*x)/(1-130*x+x^2).

Maple

seq(coeff(series(x*(1-65*x)/(1-130*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{130, -1}, {1, 65}, 30]

Prog

(Magma) I:=[1, 65]; [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)); Vec(x*(1-65*x)/(1-130*x+x^2)) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176368_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1-65*x)/(1-130*x+x^2) ).list()
a=A176368_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[1, 65];; 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. A176372.

Sequence in context: A296144 A373761 A251150 * A093265 A264541 A323316

Adjacent sequences: A176367 A176368 A176369 * A176371 A176372 A176373

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 16 2010

Status

approved