A041893 Denominators of continued fraction convergents to sqrt(468).

1, 1, 2, 3, 8, 11, 19, 30, 1279, 1309, 2588, 3897, 10382, 14279, 24661, 38940, 1660141, 1699081, 3359222, 5058303, 13475828, 18534131, 32009959, 50544090, 2154861739, 2205405829, 4360267568, 6565673397, 17491614362, 24057287759, 41548902121, 65606189880

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1298,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-36*x^4-1)*(x^8+36*x^4-1)). - Colin Barker, Nov 26 2013

a(n) = 1298*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[468], 50]] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 3 x^11 + 8 x^10 - 11 x^9 + 19 x^8 - 30 x^7 - 19 x^6 - 11 x^5 - 8 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^16 - 1298 x^8 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 8, 11, 19, 30, 1279, 1309, 2588, 3897, 10382, 14279, 24661, 38940]; [n le 16 select I[n] else 1298*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041892, A040446.

Sequence in context: A091076 A112595 A041075 * A206241 A295333 A113873

Adjacent sequences: A041890 A041891 A041892 * A041894 A041895 A041896

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved