A041167 Denominators of continued fraction convergents to sqrt(93).

1, 1, 2, 3, 14, 87, 362, 449, 811, 1260, 23491, 24751, 48242, 72993, 340214, 2114277, 8797322, 10911599, 19708921, 30620520, 570878281, 601498801, 1172377082, 1773875883, 8267880614, 51381159567, 213792518882, 265173678449, 478966197331, 744139875780

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,24302,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +14*x^14 -87*x^13 +362*x^12 -449*x^11 +811*x^10 -1260*x^9 -811*x^8 -449*x^7 -362*x^6 -87*x^5 -14*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -24302*x^10 +1). - Colin Barker, Nov 14 2013

a(n) = 24302*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[93], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 14, 87, 362, 449, 811, 1260, 23491, 24751, 48242, 72993, 340214, 2114277, 8797322, 10911599, 19708921, 30620520]; [n le 20 select I[n] else 24302*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041166, A010164, A020850, A010544.

Sequence in context: A366326 A203761 A154750 * A294380 A343261 A308128

Adjacent sequences: A041164 A041165 A041166 * A041168 A041169 A041170

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved