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A041102 Numerators of continued fraction convergents to sqrt(59). 2
7, 8, 23, 169, 361, 530, 7781, 8311, 24403, 179132, 382667, 561799, 8247853, 8809652, 25867157, 189879751, 405626659, 595506410, 8742716399, 9338222809, 27419162017, 201272356928, 429963875873 (list; graph; refs; listen; history; text; internal format)
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 A080982 A271901

Adjacent sequences:  A041099 A041100 A041101 * A041103 A041104 A041105

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)