A041729 Denominators of continued fraction convergents to sqrt(384).

1, 1, 2, 5, 47, 99, 146, 245, 9456, 9701, 19157, 48015, 451292, 950599, 1401891, 2352490, 90796511, 93149001, 183945512, 461040025, 4333305737, 9127651499, 13460957236, 22588608735, 871828089166, 894416697901, 1766244787067, 4426906272035, 41608401235382

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,9602,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -5*x^11 +47*x^10 -99*x^9 +146*x^8 -245*x^7 -146*x^6 -99*x^5 -47*x^4 -5*x^3 -2*x^2 -x -1) / ((x^4 -4*x^3 +8*x^2 +4*x +1)*(x^4 -10*x^2 +1)*(x^4 +10*x^2 +1)*(x^4 +4*x^3 +8*x^2 -4*x +1)). - Colin Barker, Nov 22 2013

a(n) = 9602*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 23 2013

Maple

convert(sqrt(384), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[384], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 9602, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 5, 47, 99, 146, 245, 9456, 9701, 19157, 48015, 451292, 950599, 1401891, 2352490}, 40] (* Harvey P. Dale, May 26 2018 *)

Crossrefs

Cf. A041728, A040364.

Sequence in context: A119715 A326965 A023273 * A078665 A163666 A093552

Adjacent sequences: A041726 A041727 A041728 * A041730 A041731 A041732

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved