A041104 Numerators of continued fraction convergents to sqrt(60).

7, 8, 23, 31, 457, 488, 1433, 1921, 28327, 30248, 88823, 119071, 1755817, 1874888, 5505593, 7380481, 108832327, 116212808, 341257943, 457470751, 6745848457, 7203319208, 21152486873, 28355806081, 418133772007, 446489578088, 1311112928183, 1757602506271

Offset

0,1

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^7-7*x^6+8*x^5-23*x^4-31*x^3-23*x^2-8*x-7) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - Colin Barker, Nov 05 2013

Maple

numtheory:-cfrac(sqrt(60), 50, 'con'):
map(numer, con[1..-2]); # Robert Israel, Jun 09 2015

Mathematica

Numerator/@Convergents[Sqrt[60], 30]  (* Harvey P. Dale, Apr 26 2011 *)
n0 := LinearRecurrence[{62, -1}, {7, 457}, 10]
n1 := LinearRecurrence[{62, -1}, {8, 488}, 10]
n2 := LinearRecurrence[{62, -1}, {23, 1433}, 10]
n3 := LinearRecurrence[{62, -1}, {31, 1921}, 10]
Flatten[MapIndexed[{n0[[#]], n1[[#]], n2[[#]], n3[[#]]} &, Range[10]]] (* Gerry Martens, Jun 09 2015 *)
LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1}, {7, 8, 23, 31, 457, 488, 1433, 1921}, 28] (* Ray Chandler, Aug 03 2015 *)

Crossrefs

Cf. A010513, A041105.

Sequence in context: A042417 A042845 A295337 * A042391 A042023 A041102

Adjacent sequences: A041101 A041102 A041103 * A041105 A041106 A041107

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 05 2013

Status

approved