A176367 y-values in the solution to x^2 - 62*y^2 = 1.

0, 8, 1008, 127000, 16000992, 2015997992, 253999746000, 32001951998008, 4031991952003008, 507998984000381000, 64003839992096002992, 8063975840020095995992, 1015996952002539999492000

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A174763.

Links

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

Index entries for linear recurrences with constant coefficients, signature (126,-1).

Formula

a(n) = 126*a(n-1) - a(n-2) with a(1)=0, a(2)=8.

G.f.: 8*x^2/(1-126*x+x^2).

Maple

seq(coeff(series(8*x^2/(1-126*x+x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Dec 07 2019

Mathematica

LinearRecurrence[{126, -1}, {0, 8}, 20]

Prog

(Magma) I:=[0, 8]; [n le 2 select I[n] else 126*Self(n-1)-Self(n-2): n in [1..20]];
(PARI) my(x='x+O('x^20)); concat([0], Vec(8*x^2/(1-126*x+x^2))) \\ G. C. Greubel, Dec 07 2019
(Sage)
def A176367_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 8*x^2/(1-126*x+x^2) ).list()
a=A176367_list(20); a[1:] # G. C. Greubel, Dec 07 2019
(GAP) a:=[0, 8];; for n in [3..20] do a[n]:=126*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 07 2019

Crossrefs

Cf. A174763.

Sequence in context: A019545 A046242 A260028 * A298669 A007117 A291831

Adjacent sequences: A176364 A176365 A176366 * A176368 A176369 A176370

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 16 2010

Status

approved