A228210 x-values in the solutions to x^2 - 5y^2 = 44.

7, 8, 13, 17, 32, 43, 83, 112, 217, 293, 568, 767, 1487, 2008, 3893, 5257, 10192, 13763, 26683, 36032, 69857, 94333, 182888, 246967, 478807, 646568, 1253533, 1692737, 3281792, 4431643, 8591843, 11602192, 22493737, 30374933, 58889368, 79522607, 154174367

Offset: 1

Author

Colin Barker, Aug 16 2013

Keywords

• nonn
• easy

Comments

Also values of x (or y) in the solutions to x^2 - 3xy + y^2 + 55 = 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Project Euler, Problem 140: Modified Fibonacci golden nuggets
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Crossrefs

Cf. A228208.

Programs

Magma

I:=[7,8,13,17]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 17 2013

Mathematica

CoefficientList[Series[-(x - 1) (7 x^2 + 15 x + 7) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{0,3,0,-1},{7,8,13,17},40] (* Harvey P. Dale, Jun 01 2020 *)

PARI

Vec(-x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))

Formula

G.f.: -x*(x-1)*(7*x^2+15*x+7) / ((x^2-x-1)*(x^2+x-1)).

a(n) = 3*a(n-2)-a(n-4).