A041983 Denominators of continued fraction convergents to sqrt(514).

1, 1, 3, 67, 137, 204, 9113, 9317, 27747, 619751, 1267249, 1887000, 84295249, 86182249, 256659747, 5732696683, 11722053113, 17454749796, 779731044137, 797185793933, 2374102632003, 53027443697999, 108428990028001, 161456433726000, 7212512073972001

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,9250,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-x^9+3*x^8-67*x^7+137*x^6-204*x^5-137*x^4-67*x^3-3*x^2-x-1) / (x^12-9250*x^6+1). - Colin Barker, Nov 28 2013

a(n) = 9250*a(n-6) - a(n-12). - Wesley Ivan Hurt, Apr 18 2023

Mathematica

Denominator[Convergents[Sqrt[514], 30]] (* Vincenzo Librandi, Jan 11 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 9250, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 67, 137, 204, 9113, 9317, 27747, 619751, 1267249, 1887000}, 30] (* Harvey P. Dale, Sep 15 2019 *)

Prog

(Magma) I:=[1, 1, 3, 67, 137, 204, 9113, 9317, 27747, 619751, 1267249, 1887000]; [n le 12 select I[n] else 9250*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Jan 11 2014

Crossrefs

Cf. A041982, A040491.

Sequence in context: A110716 A142035 A142926 * A263549 A225191 A370659

Adjacent sequences: A041980 A041981 A041982 * A041984 A041985 A041986

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved