A041304 Numerators of continued fraction convergents to sqrt(165).

12, 13, 77, 167, 912, 1079, 26808, 27887, 166243, 360373, 1968108, 2328481, 57851652, 60180133, 358752317, 777684767, 4247176152, 5024860919, 124843838208, 129868699127, 774187333843, 1678243366813, 9165404167908, 10843647534721, 269412945001212

Offset: 0

Author

N. J. A. Sloane

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 (0,0,0,0,0,2158,0,0,0,0,0,-1).

Crossrefs

Cf. A041305.

Programs

Mathematica

Numerator[Convergents[Sqrt[165],30]] (* Harvey P. Dale, Dec 25 2012 *)

Formula

G.f.: -(x^11 -12*x^10 +13*x^9 -77*x^8 +167*x^7 -912*x^6 -1079*x^5 -912*x^4 -167*x^3 -77*x^2 -13*x -12) / ((x^4 -13*x^2 +1)*(x^8 +13*x^6 +168*x^4 +13*x^2 +1)). - Colin Barker, Nov 06 2013

Extensions

More terms from Colin Barker, Nov 06 2013