A174779 y-values in the solution to x^2 - 42*y^2 = 1.

0, 2, 52, 1350, 35048, 909898, 23622300, 613269902, 15921395152, 413343004050, 10730996710148, 278592571459798, 7232675861244600, 187770979820899802, 4874812799482150252, 126557361806715006750, 3285616594175108025248

Offset

1,2

Comments

The corresponding values of x of this Pell equation are in A097308.

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-1).

Formula

a(n) = 26*a(n-1)-a(n-2) with a(1)=0, a(2)=2.

G.f.: 2*x^2/(1-26*x+x^2).

Mathematica

LinearRecurrence[{26, -1}, {0, 2}, 30]
With[{c=2*Sqrt[42]}, Table[-((13-c)^n-(13+c)^n)/c, {n, 0, 20}]]//Simplify (* Harvey P. Dale, Nov 05 2022 *)

Prog

(Magma) I:=[0, 2]; [n le 2 select I[n] else 26*Self(n-1)-Self(n-2): n in [1..20]];

Crossrefs

Cf. A097308.

Sequence in context: A284767 A101930 A297756 * A215744 A099882 A216611

Adjacent sequences: A174776 A174777 A174778 * A174780 A174781 A174782

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 15 2010

Status

approved