A041428 Numerators of continued fraction convergents to sqrt(230).
15, 91, 2745, 16561, 499575, 3014011, 90919905, 548533441, 16546923135, 99830072251, 3011449090665, 18168524616241, 548067187577895, 3306571650083611, 99745216690086225, 601777871790600961
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,182,0,-1).
Crossrefs
Cf. A041429.
Programs
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Mathematica
Numerator[Convergents[Sqrt[230], 20]] (* Harvey P. Dale, Jun 12 2012 *) CoefficientList[Series[-(x^3 - 15 x^2 - 91 x - 15)/(x^4 -182 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 02 2013 *)
Formula
G.f.: -(x^3 -15*x^2 -91*x -15)/(x^4 -182*x^2 +1). - Vincenzo Librandi, Nov 02 2013
a(n) = 182*a(n-2) - a(n-4). - Wesley Ivan Hurt, May 04 2024