A175014 y-values in the solution to x^2-55*y^2=1.

0, 12, 2136, 380196, 67672752, 12045369660, 2144008126728, 381621401187924, 67926465403323744, 12090529220390438508, 2152046274764094730680, 383052146378788471622532, 68181130009149583854080016

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A174758.

Links

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

Index entries for linear recurrences with constant coefficients, signature (178,-1).

Formula

a(n) = 178*a(n-1)-a(n-2) with a(1)=0, a(2)=12.

G.f.: 12*x^2/(1-178*x+x^2).

a(n) = ((89+12*sqrt(55))^(n-1) - (89-12*sqrt(55))^(n-1))/(2*sqrt(55)). - Alan Michael Gómez Calderón, Oct 06 2023

Mathematica

LinearRecurrence[{178, -1}, {0, 12}, 30]

Prog

(Magma) I:=[0, 12]; [n le 2 select I[n] else 178*Self(n-1)-Self(n-2): n in [1..20]];

Crossrefs

Cf. A174758.

Sequence in context: A342964 A009063 A012675 * A101812 A064074 A005249

Adjacent sequences: A175011 A175012 A175013 * A175015 A175016 A175017

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 15 2010

Status

approved