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

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 (0,488,0,-1).

Crossrefs

Cf. A042415.

Programs

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

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 *)

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