A041477 Denominators of continued fraction convergents to sqrt(254).

1, 1, 15, 16, 495, 511, 7649, 8160, 252449, 260609, 3900975, 4161584, 128748495, 132910079, 1989489601, 2122399680, 65661480001, 67783879681, 1014635795535, 1082419675216, 33487226052015, 34569645727231, 517462266233249, 552031911960480, 17078419625047649

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,510,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+16*x^2+1) / (x^8-510*x^4+1). - Colin Barker, Nov 18 2013

a(n) = 510*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[254], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 510, 0, 0, 0, -1}, {1, 1, 15, 16, 495, 511, 7649, 8160}, 30] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(Magma) I:=[1, 1, 15, 16, 495, 511, 7649, 8160]; [n le 8 select I[n] else 510*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041476, A040238.

Sequence in context: A033051 A041111 A041476 * A041478 A042099 A156530

Adjacent sequences: A041474 A041475 A041476 * A041478 A041479 A041480

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved