A041105 Denominators of continued fraction convergents to sqrt(60).

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

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: A317856 A331725 A067093 * A196442 A349587 A278035

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