A176374 y-values in the solution to x^2 - 67*y^2 = 1.

0, 5967, 582880428, 56938091722785, 5561940551265649512, 543312600752895615207423, 53072948086383914724656258820, 5184377860327013725210426371365457, 506430766855111060647071374935807042768

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A176373.

Links

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

Index entries for linear recurrences with constant coefficients, signature (97684,-1).

Formula

a(n) = 97684*a(n-1) - a(n-2) with a(1)=0, a(2)=5967.

From Bruno Berselli, Dec 14 2011: (Start)

G.f.: 5967*x^2/(1-97684*x+x^2).

a(n) = ((221+27*r)^(2*n-2) - (221-27*r)^(2*n-2))/(2^n*r), where r=sqrt(67). (End)

Maple

seq(coeff(series(5967*x^2/(1-97684*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{97684, -1}, {0, 5967}, 20]

Prog

(Magma) I:=[0, 5967]; [n le 2 select I[n] else 97684*Self(n-1)-Self(n-2): n in [1..10]];
(Maxima) makelist(expand(((221+27*sqrt(67))^(2*n-2)-(221-27*sqrt(67))^(2*n-2))/(2^n*sqrt(67))), n, 1, 9); /* Bruno Berselli, Dec 14 2011 */
(PARI) my(x='x+O('x^15)); concat([0], Vec(5967*x^2/(1-97684*x+x^2)) ) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176374_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 5967*x^2/(1-97684*x+x^2) ).list()
a=A176374_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[0, 5967];; for n in [3..15] do a[n]:=97684*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 08 2019

Crossrefs

Cf. A176373.

Sequence in context: A266038 A032658 A157666 * A282191 A328327 A364861

Adjacent sequences: A176371 A176372 A176373 * A176375 A176376 A176377

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 16 2010

Status

approved