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A228210
x-values in the solutions to x^2 - 5y^2 = 44.
2
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
1,1
COMMENTS
Also values of x (or y) in the solutions to x^2 - 3xy + y^2 + 55 = 0.
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).
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 *)
PROG
(PARI) Vec(-x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
(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
CROSSREFS
Cf. A228208.
Sequence in context: A308887 A308833 A025156 * A045765 A118068 A060754
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Aug 16 2013
STATUS
approved