A228209 x-values in the solutions to x^2 - 10*y^2 = 9.

3, 7, 13, 57, 253, 487, 2163, 9607, 18493, 82137, 364813, 702247, 3119043, 13853287, 26666893, 118441497, 526060093, 1012639687, 4497657843, 19976430247, 38453641213, 170792556537, 758578289293, 1460225726407, 6485619490563, 28805998562887, 55450123962253

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Pell Equation

Index entries for linear recurrences with constant coefficients, signature (0,0,38,0,0,-1).

Formula

G.f.: -x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3) / (x^6-38*x^3+1).

a(n) = 38*a(n-3)-a(n-6).

Mathematica

CoefficientList[Series[-(7 x^6 + 13 x^5 + 57 x^4 - 13 x^3 - 7 x^2 - 3 x) / (x^6 - 38 x^3 + 1), {x, 1, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{0, 0, 38, 0, 0, -1}, {3, 7, 13, 57, 253, 487}, 30] (* Harvey P. Dale, Jan 06 2014 *)

Prog

(PARI) Vec(-x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3)/(x^6-38*x^3+1) + O(x^100))
(Magma) I:=[3, 7, 13, 57, 253, 487]; [n le 6 select I[n] else 38*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Aug 17 2013

Crossrefs

Cf. A075836.

Sequence in context: A257716 A103564 A083201 * A176903 A004060 A028491

Adjacent sequences: A228206 A228207 A228208 * A228210 A228211 A228212

Keyword

nonn,easy

Author

Colin Barker, Aug 16 2013

Extensions

a(1)=3 prepended by Max Alekseyev, Sep 04 2013

Status

approved