%I #18 Jul 09 2025 02:18:02

%S 1,3,13,16,29,219,248,467,2116,6815,329236,994523,4307328,5301851,

%T 9609179,72566104,82175283,154741387,701140831,2258163880,

%U 109093007071,329537185093,1427241747443,1756778932536,3184020679979,24044923692389,27228944372368

%N Denominators of continued fraction convergents to sqrt(591).

%H Vincenzo Librandi, <a href="/A042133/b042133.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,331352,0,0,0,0,0,0,0,0,0,-1).

%F 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

%F a(n) = 331352*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Jan 15 2014

%t Denominator[Convergents[Sqrt[591],30]] (* _Harvey P. Dale_, May 25 2013 *)

%t 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 *)

%Y Cf. A042132, A040566.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 02 2013