A228205 x-values in the solution to x^2 - 13y^2 = 108.

11, 15, 24, 41, 80, 141, 249, 440, 869, 1536, 2715, 4799, 9479, 16755, 29616, 52349, 103400, 182769, 323061, 571040, 1127921, 1993704, 3524055, 6229091, 12303731, 21747975, 38441544, 67948961, 134213120, 237234021, 419332929, 741209480, 1464040589

Offset

1,1

Comments

This equation is used for worked examples in the Robertson link.

Links

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

John P. Robertson, Solving the generalized Pell equation x^2 - Dy^2 = N

Index entries for linear recurrences with constant coefficients, signature (0,0,0,11,0,0,0,-1).

Formula

G.f.: -x*(x-1)*(11*x^6+26*x^5+50*x^4+91*x^3+50*x^2+26*x+11) / ((x^4-3*x^2-1)*(x^4+3*x^2-1)).

a(n) = 11*a(n-4)-a(n-8).

Mathematica

CoefficientList[Series[-(x - 1) (11 x^6 + 26 x^5 + 50 x^4 + 91 x^3 + 50 x^2 + 26 x + 11) / ((x^4 - 3 x^2 - 1) (x^4 + 3 x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)

Prog

(PARI) Vec(-x*(x-1)*(11*x^6+26*x^5+50*x^4+91*x^3+50*x^2+26*x+11)/((x^4-3*x^2-1)*(x^4+3*x^2-1)) + O(x^100))

Crossrefs

Cf. A228206.

Sequence in context: A285271 A087142 A158019 * A343416 A256498 A054280

Adjacent sequences: A228202 A228203 A228204 * A228206 A228207 A228208

Keyword

nonn,easy

Author

Colin Barker, Aug 16 2013

Status

approved