A228206 y-values in the solution to x^2 - 13y^2 = 108.

1, 3, 6, 11, 22, 39, 69, 122, 241, 426, 753, 1331, 2629, 4647, 8214, 14519, 28678, 50691, 89601, 158378, 312829, 552954, 977397, 1727639, 3412441, 6031803, 10661766, 18845651, 37224022, 65796879, 116302029, 205574522, 406051801, 717733866, 1268660553

Offset

1,2

Comments

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

Links

Colin Barker, 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)*(x^6+2*x^5+4*x^4+7*x^3+4*x^2+2*x+1) / ((x^4-3*x^2-1)*(x^4+3*x^2-1)).

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

Mathematica

LinearRecurrence[{0, 0, 0, 11, 0, 0, 0, -1}, {1, 3, 6, 11, 22, 39, 69, 122}, 50] (* Harvey P. Dale, Jul 07 2022 *)

Prog

(PARI) Vec(x*(x+1)*(x^6+2*x^5+4*x^4+7*x^3+4*x^2+2*x+1)/((x^4-3*x^2-1)*(x^4+3*x^2-1)) + O(x^100))

Crossrefs

Cf. A228205

Sequence in context: A191581 A192896 A115030 * A195734 A018177 A103322

Adjacent sequences: A228203 A228204 A228205 * A228207 A228208 A228209

Keyword

nonn,easy

Author

Colin Barker, Aug 16 2013

Status

approved