A041264 Numerators of continued fraction convergents to sqrt(145).

12, 289, 6948, 167041, 4015932, 96549409, 2321201748, 55805391361, 1341650594412, 32255419657249, 775471722368388, 18643576756498561, 448221313878333852, 10775955109836511009, 259071143949954598068, 6228483409908746864641, 149742672981759879349452

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (24,1).

Crossrefs

Cf. A041265.

Programs

Mathematica

Numerator[Convergents[Sqrt[145], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

Formula

a(n) = 24*a(n-1)+a(n-2) for n>1; a(0)=12, a(1)=289. G.f.: (12+x)/(1-24*x-x^2). [Philippe Deléham, Nov 21 2008]

Extensions

More terms from Colin Barker, Nov 06 2013