A042414 Numerators of continued fraction convergents to sqrt(735).

27, 244, 13203, 119071, 6443037, 58106404, 3144188853, 28355806081, 1534357717227, 13837575261124, 748763421817923, 6752708371622431, 365395015489429197, 3295307847776485204, 178312018795419630213

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,488,0,-1).

Formula

G.f.: (27 +244*x +27*x^2 -x^3)/(1 -488*x^2 +x^4). - Vincenzo Librandi, Nov 23 2013

a(n) = 488*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[735], 30]] (* or *) CoefficientList[Series[(27 + 244 x + 27 x^2 - x^3)/(1 - 488 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[27, 244, 13203, 119071]; [n le 4 select I[n] else 488*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042415.

Sequence in context: A345054 A074117 A030509 * A099226 A016107 A101379

Adjacent sequences: A042411 A042412 A042413 * A042415 A042416 A042417

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved