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

0,1

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).

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]

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 *)

Crossrefs

Cf. A010512, A041103.

Sequence in context: A041104 A042391 A042023 * A136116 A329635 A080982

Adjacent sequences: A041099 A041100 A041101 * A041103 A041104 A041105

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved