A041903 Denominators of continued fraction convergents to sqrt(473).

1, 1, 3, 4, 171, 175, 521, 696, 29753, 30449, 90651, 121100, 5176851, 5297951, 15772753, 21070704, 900742321, 921813025, 2744368371, 3666181396, 156723987003, 160390168399, 477504323801, 637894492200, 27269072996201, 27906967488401, 83083007973003

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, 174, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-174*x^4+1). - Colin Barker, Nov 27 2013

a(n) = 174*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[473], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 3, 4, 171, 175, 521, 696]; [n le 8 select I[n] else 174*Self(n-4)-Self(n-8): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041902, A040451.

Sequence in context: A370385 A041595 A041741 * A156513 A082213 A097172

Adjacent sequences: A041900 A041901 A041902 * A041904 A041905 A041906

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 27 2013

Status

approved