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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010513, A041105.

Programs

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 *)

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

Extensions

More terms from Colin Barker, Nov 05 2013