A082962 Numerators of continued fraction convergents to (sqrt(37)-4)/3.

0, 1, 2, 7, 9, 25, 84, 109, 302, 1015, 1317, 3649, 12264, 15913, 44090, 148183, 192273, 532729, 1790460, 2323189, 6436838, 21633703, 28070541, 77774785, 261394896, 339169681, 939734258, 3158372455, 4098106713, 11354585881, 38161864356

Offset: 0

Author

Gary W. Adamson, May 27 2003

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 12, 0, 0, 1).

Crossrefs

Denominators are A082975.

Programs

Mathematica

t = Join[{0}, Flatten[ Table[{1, 2, 3}, {12}]]]; Rest[ Table[ Numerator[ FromContinuedFraction[ Take[t, n]]], {n, 31}]] (* Robert G. Wilson v, Feb 12 2005 *)
Numerator[Convergents [(Sqrt[37]-4)/3, 30]] (* Vincenzo Librandi, Feb 01 2014 *)

Formula

Empirical g.f.: x*(1+2*x+7*x^2-3*x^3+x^4)/(1-12*x^3-x^6). - Colin Barker, Jan 04 2012

Extensions

Edited by Don Reble, Nov 04 2005

Prepended a(0)=0 from Vincenzo Librandi, Feb 01 2014