A041804 Numerators of continued fraction convergents to sqrt(423).
20, 21, 41, 144, 617, 1995, 2612, 4607, 186892, 191499, 378391, 1326672, 5685079, 18381909, 24066988, 42448897, 1722022868, 1764471765, 3486494633, 12223955664, 52382317289, 169370907531, 221753224820, 391124132351, 15866718518860, 16257842651211
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 9214, 0, 0, 0, 0, 0, 0, 0, -1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[423], 30]] (* Harvey P. Dale, Oct 09 2013 *)
Formula
G.f.: -(x^15 -20*x^14 +21*x^13 -41*x^12 +144*x^11 -617*x^10 +1995*x^9 -2612*x^8 -4607*x^7 -2612*x^6 -1995*x^5 -617*x^4 -144*x^3 -41*x^2 -21*x -20) / ((x^8 -96*x^4 +1)*(x^8 +96*x^4 +1)). - Colin Barker, Nov 25 2013
Extensions
More terms from Colin Barker, Nov 25 2013