A041916 Numerators of continued fraction convergents to sqrt(480).

21, 22, 219, 241, 10341, 10582, 105579, 116161, 4984341, 5100502, 50888859, 55989361, 2402442021, 2458431382, 24528324459, 26986755841, 1157972069781, 1184958825622, 11822601500379, 13007560326001

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• frac
• less

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,482,0,0,0,-1).

Crossrefs

Cf. A041917.

Programs

Mathematica

Numerator[Convergents[Sqrt[480],30]] (* Harvey P. Dale, Aug 14 2012 *)
CoefficientList[Series[- (x^7 - 21 x^6 + 22 x^5 - 219 x^4 - 241 x^3 - 219 x^2 - 22 x - 21)/((x^4 - 22 x^2 + 1) (x^4 + 22 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 27 2013 *)

Formula

a(n) = 482*a(n-4)-a(n-8). G.f.: -(x^7-21*x^6+22*x^5-219*x^4-241*x^3-219*x^2-22*x-21)/((x^4-22*x^2+1)*(x^4+22*x^2+1)). [Colin Barker, Jul 16 2012]