A176373 x-values in the solution to x^2 - 67*y^2 = 1.

1, 48842, 4771081927, 466058366908226, 45526445508292066657, 4447205302565943872414162, 434420802730325215724612934151, 42435961689461883070277145987192122, 4145314481238973783106627512888262311297

Offset

1,2

Comments

The corresponding values of y of this Pell equation are in A176374.

Links

G. C. Greubel, 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)=1, a(2)=48842.

From Bruno Berselli, Dec 14 2011: (Start)

G.f.: x*(1-48842*x)/(1-97684*x+x^2).

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

Maple

seq(coeff(series(x*(1-48842*x)/(1-97684*x+x^2), x, n+1), x, n), n = 1..15); # G. C. Greubel, Dec 08 2019

Mathematica

LinearRecurrence[{97684, -1}, {1, 48842}, 15] (* G. C. Greubel, Dec 08 2019 *)

Prog

(Maxima) makelist(expand(((221+27*sqrt(67))^(2*n-2)+(221-27*sqrt(67))^(2*n-2))/2^n), n, 1, 9); /* Bruno Berselli, Dec 14 2011 */
(Magma) I:=[1, 48842]; [n le 2 select I[n] else 97684*Self(n-1)-Self(n-2): n in [1..15]]; // G. C. Greubel, Dec 08 2019
(PARI) my(x='x+O('x^15)); Vec(x*(1-48842*x)/(1-97684*x+x^2)) \\ G. C. Greubel, Dec 08 2019
(Sage)
def A176368_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1-48842*x)/(1-97684*x+x^2) ).list()
a=A176368_list(15); a[1:] # G. C. Greubel, Dec 08 2019
(GAP) a:=[1, 48842];; 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. A176374.

Sequence in context: A175278 A336189 A157667 * A237087 A061737 A045938

Adjacent sequences: A176370 A176371 A176372 * A176374 A176375 A176376

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 16 2010

Status

approved