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A041229
Denominators of continued fraction convergents to sqrt(126).
2
1, 4, 9, 40, 889, 3596, 8081, 35920, 798321, 3229204, 7256729, 32256120, 716891369, 2899821596, 6516534561, 28965959840, 643767651041, 2604036564004, 5851840779049, 26011399680200, 578102633743449, 2338421934653996, 5254946503051441, 23358207946859760
OFFSET
0,2
FORMULA
G.f.: (1 + 4*x + 9*x^2 + 40*x^3 - 9*x^4 + 4*x^5 - x^6)/(1 - 898*x^4 + x^8). - Vincenzo Librandi, Dec 13 2013
a(n) = 898*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[126], 30]] (* or *) CoefficientList[Series[(1 + 4 x + 9 x^2 + 40 x^3 - 9 x^4 + 4 x^5 - x^6)/(1 - 898 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 898, 0, 0, 0, -1}, {1, 4, 9, 40, 889, 3596, 8081, 35920}, 30] (* Harvey P. Dale, Aug 20 2017 *)
PROG
(Magma) I:=[1, 4, 9, 40, 889, 3596, 8081, 35920]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Cf. A041228.
Sequence in context: A085110 A374939 A013459 * A042887 A053908 A149165
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 13 2013
STATUS
approved