A042675 - OEIS

%I #19 May 11 2024 03:27:34

%S 1,2,9,263,1061,2385,139391,281167,1264059,36938878,149019571,

%T 334978020,19577744731,39490467482,177539614659,5188139292593,

%U 20930096785031,47048332862655,2749733402819021,5546515138500697,24935793956821809,728684539886333158

%N Denominators of continued fraction convergents to sqrt(867).

%H Vincenzo Librandi, <a href="/A042675/b042675.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 140452, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^10 -2*x^9 +9*x^8 -263*x^7 +1061*x^6 -2385*x^5 -1061*x^4 -263*x^3 -9*x^2 -2*x -1) / ((x^4 -52*x^2 +1)*(x^8 +52*x^6 +2703*x^4 +52*x^2 +1)). - _Colin Barker_, Dec 20 2013

%F a(n) = 140452*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 20 2013

%t Denominator[Convergents[Sqrt[867], 30]] (* _Vincenzo Librandi_, Dec 20 2013 *)

%t LinearRecurrence[{0,0,0,0,0,140452,0,0,0,0,0,-1},{1,2,9,263,1061,2385,139391,281167,1264059,36938878,149019571,334978020},30] (* _Harvey P. Dale_, May 11 2024 *)

%o (Magma) I:=[1,2,9,263,1061,2385,139391,281167,1264059, 36938878,149019571,334978020]; [n le 12 select I[n] else 140452*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013

%Y Cf. A042674, A040837.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 20 2013