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A041104 Numerators of continued fraction convergents to sqrt(60). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)