A042004 Numerators of continued fraction convergents to sqrt(525).

22, 23, 252, 527, 5522, 6049, 271678, 277727, 3048948, 6375623, 66805178, 73180801, 3286760422, 3359941223, 36886172652, 77132286527, 808209037922, 885341324449, 39763227313678, 40648568638127

Offset

0,1

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, 12098, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11-22*x^10+23*x^9-252*x^8+527*x^7-5522*x^6-6049*x^5-5522*x^4-527*x^3-252*x^2-23*x-22)/(x^12-12098*x^6+1). - Vincenzo Librandi, Nov 13 2013

a(n) = 12098*a(n-6)-a(n-12). - Vincenzo Librandi, Nov 13 2013

Mathematica

Numerator[Convergents[Sqrt[525], 30]] (* or *) CoefficientList[Series[-(x^11 - 22 x^10 + 23 x^9 - 252 x^8 + 527 x^7 - 5522 x^6 - 6049 x^5 - 5522 x^4 - 527 x^3 - 252 x^2 - 23 x - 22)/(x^12 - 12098 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)

Prog

(Magma) I:=[22, 23, 252, 527, 5522, 6049, 271678, 277727, 3048948, 6375623, 66805178, 73180801]; [n le 12 select I[n] else 12098*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 13 2013

Crossrefs

Cf. A042005.

Sequence in context: A042000 A042002 A119603 * A042006 A042008 A042009

Adjacent sequences: A042001 A042002 A042003 * A042005 A042006 A042007

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved