A042133 Denominators of continued fraction convergents to sqrt(591).

1, 3, 13, 16, 29, 219, 248, 467, 2116, 6815, 329236, 994523, 4307328, 5301851, 9609179, 72566104, 82175283, 154741387, 701140831, 2258163880, 109093007071, 329537185093, 1427241747443, 1756778932536, 3184020679979, 24044923692389, 27228944372368

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,331352,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -3*x^17 +13*x^16 -16*x^15 +29*x^14 -219*x^13 +248*x^12 -467*x^11 +2116*x^10 -6815*x^9 -2116*x^8 -467*x^7 -248*x^6 -219*x^5 -29*x^4 -16*x^3 -13*x^2 -3*x -1) / (x^20 -331352*x^10 +1). - Colin Barker, Dec 02 2013

a(n) = 331352*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[591], 30]] (* Harvey P. Dale, May 25 2013 *)
CoefficientList[Series[-(x^18 - 3 x^17 + 13 x^16 - 16 x^15 + 29 x^14 - 219 x^13 + 248 x^12 - 467 x^11 + 2116 x^10 - 6815 x^9 - 2116 x^8 - 467 x^7 - 248 x^6 - 219 x^5 - 29 x^4 - 16 x^3 - 13 x^2 - 3 x - 1)/(x^20 - 331352 x^10 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 15 2014 *)

Crossrefs

Cf. A042132, A040566.

Sequence in context: A063674 A273678 A022124 * A041297 A041815 A042589

Adjacent sequences: A042130 A042131 A042132 * A042134 A042135 A042136

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved