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A041105 Denominators of continued fraction convergents to sqrt(60). 3
1, 1, 3, 4, 59, 63, 185, 248, 3657, 3905, 11467, 15372, 226675, 242047, 710769, 952816, 14050193, 15003009, 44056211, 59059220, 870885291, 929944511, 2730774313, 3660718824, 53980837849, 57641556673, 169263951195, 226905507868, 3345941061347, 3572846569215 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Interspersion of 4 linear recurrences with constant coefficients. - Gerry Martens, Jun 10 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,62,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - Colin Barker, Nov 12 2013

a(n) = 62*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

MAPLE

numtheory:-cfrac(sqrt(60), 100, 'con', 'den'):

den[1..-2]; # Robert Israel, Jun 09 2015

MATHEMATICA

Denominator[Convergents[Sqrt[60], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

d0 := LinearRecurrence[{62, -1}, {1, 59}, 20]

d1 := LinearRecurrence[{62, -1}, {1, 63}, 20] (* A258684  *)

d2 := LinearRecurrence[{62, -1}, {3, 185}, 20]

d3 := LinearRecurrence[{62, -1}, {4, 248}, 20]

Flatten[MapIndexed[{d0[[#]] , d1[[#]], d2[[#]] , d3[[#]]} &,

  Range[10]]] (* Gerry Martens, Jun 09 2015 *)

LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1}, {1, 1, 3, 4, 59, 63, 185, 248}, 30] (* Ray Chandler, Aug 03 2015 *)

PROG

(MAGMA) I:=[1, 1, 3, 4, 59, 63, 185, 248]; [n le 8 select I[n] else 62*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A041104, A040052, A020817, A010513.

Cf. A258684.

Sequence in context: A166850 A317856 A067093 * A196442 A278035 A079076

Adjacent sequences:  A041102 A041103 A041104 * A041106 A041107 A041108

KEYWORD

nonn,cofr,easy,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Colin Barker, Nov 12 2013

STATUS

approved

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Last modified September 18 07:50 EDT 2019. Contains 327168 sequences. (Running on oeis4.)