A228207 x-values in the solution to x^2 - 20*y^2 = 176.
14, 16, 26, 34, 64, 86, 166, 224, 434, 586, 1136, 1534, 2974, 4016, 7786, 10514, 20384, 27526, 53366, 72064, 139714, 188666, 365776, 493934, 957614, 1293136, 2507066, 3385474, 6563584, 8863286, 17183686, 23204384, 44987474, 60749866, 117778736, 159045214
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).
Programs
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Magma
I:=[14,16,26,34]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 17 2013
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Mathematica
CoefficientList[Series[-2 (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},{14,16,26,34},50] (* Harvey P. Dale, May 25 2023 *) -
PARI
Vec(-2*x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
Formula
G.f.: -2*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).
a(n) = 2*A228210(n). - Hugo Pfoertner, Feb 11 2024