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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A041805, A040402.

Programs

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