A174771 y-values in the solution to x^2 - 31*y^2 = 1.

0, 273, 829920, 2522956527, 7669787012160, 23316149994009873, 70881088312003001760, 215478485152339131340527, 655054523982022647272200320, 1991365537426863695368357632273

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A174746.

The first solution to the equation x^2 - 31*y^2 = 1 is (X(1), Y(1)) = (1, 0) and the other solutions are defined by: (X(n), Y(n)) = (1520*X(n-1) + 8463*Y(n-1), 273*X(n-1) + 1520*Y(n-1)) with n >= 2. - Mohamed Bouhamida, Jan 16 2020

Links

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

Index entries for linear recurrences with constant coefficients, signature (3040,-1).

Formula

a(n) = 3040*a(n-1) - a(n-2) with a(1)=0, a(2)=273.

G.f.: 273*x^2/(1-3040*x+x^2).

Mathematica

LinearRecurrence[{3040, -1}, {0, 273}, 30]

Prog

(Magma) I:=[0, 273]; [n le 2 select I[n] else 3040*Self(n-1)-Self(n-2): n in [1..20]];

Crossrefs

Cf. A174746.

Sequence in context: A225702 A307537 A295455 * A031417 A361797 A260289

Adjacent sequences: A174768 A174769 A174770 * A174772 A174773 A174774

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 14 2010

Status

approved