A041485 - OEIS

%I #21 Jul 09 2025 00:54:27

%S 1,10,11,32,107,460,1487,3434,4921,52644,1689529,16947934,18637463,

%T 54222860,181306043,779447032,2519647139,5818741310,8338388449,

%U 89202625800,2862822414049,28717426766290,31580249180339,91877925126968,307214024561243,1320734023371940

%N Denominators of continued fraction convergents to sqrt(259).

%H Vincenzo Librandi, <a href="/A041485/b041485.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1694450, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^18 -10*x^17 +11*x^16 -32*x^15 +107*x^14 -460*x^13 +1487*x^12 -3434*x^11 +4921*x^10 -52644*x^9 -4921*x^8 -3434*x^7 -1487*x^6 -460*x^5 -107*x^4 -32*x^3 -11*x^2 -10*x -1) / (x^20 -1694450*x^10 +1). - _Colin Barker_, Nov 18 2013

%F a(n) = 1694450*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 18 2013

%t Denominator[Convergents[Sqrt[259], 30]] (* _Vincenzo Librandi_, Dec 18 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,1694450,0,0,0,0,0,0,0,0,0,-1},{1,10,11,32,107,460,1487,3434,4921,52644,1689529,16947934,18637463,54222860,181306043,779447032,2519647139,5818741310,8338388449,89202625800},40] (* _Harvey P. Dale_, Aug 03 2021 *)

%o (Magma) I:=[1,10,11,32,107,460,1487,3434,4921,52644, 1689529,16947934,18637463,54222860,181306043,779447032, 2519647139,5818741310,8338388449,89202625800]; [n le 20 select I[n] else 1694450*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 18 2013

%Y Cf. A041484, A040242.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Nov 18 2013