A041102 Numerators of continued fraction convergents to sqrt(59).

7, 8, 23, 169, 361, 530, 7781, 8311, 24403, 179132, 382667, 561799, 8247853, 8809652, 25867157, 189879751, 405626659, 595506410, 8742716399, 9338222809, 27419162017, 201272356928, 429963875873

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 (0,0,0,0,0,1060,0,0,0,0,0,-1).

Crossrefs

Cf. A010512, A041103.

Programs

Mathematica

Numerator[Convergents[Sqrt[59],40]] (* or *) LinearRecurrence[ {0,0,0,0,0,1060,0,0,0,0,0,-1},{7,8,23,169,361,530,7781,8311,24403,179132,382667,561799},40] (* Harvey P. Dale, Nov 25 2012 *)
CoefficientList[Series[- (x^11 - 7 x^10 + 8 x^9 - 23 x^8 + 169 x^7 - 361 x^6 - 530 x^5 - 361 x^4 - 169 x^3 - 23 x^2 - 8 x - 7)/(x^12 - 1060 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 25 2013 *)

Formula

a(n) = 1060*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-23*x^8+169*x^7-361*x^6-530*x^5-361*x^4-169*x^3-23*x^2-8*x-7)/(x^12-1060*x^6+1). [Colin Barker, Jul 18 2012]