A041135 - OEIS

%I #22 Jun 13 2015 00:49:22

%S 1,1,3,4,7,39,163,854,1017,1871,4759,6630,110839,117469,345777,463246,

%T 809023,4508361,18842467,98720696,117563163,216283859,550130881,

%U 766414740,12812766721,13579181461,39971129643,53550311104,93521440747,521157514839,2178151500103

%N Denominators of continued fraction convergents to sqrt(76).

%H Vincenzo Librandi, <a href="/A041135/b041135.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 (0,0,0,0,0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,0,0,0,0,-1).

%F a(n) = 115598*a(n-12)-a(n-24). G.f.: -(x^22 -x^21 +3*x^20 -4*x^19 +7*x^18 -39*x^17 +163*x^16 -854*x^15 +1017*x^14 -1871*x^13 +4759*x^12 -6630*x^11 -4759*x^10 -1871*x^9 -1017*x^8 -854*x^7 -163*x^6 -39*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/((x^12-340*x^6+1)*(x^12+340*x^6+1)). [_Colin Barker_, Jul 19 2012]

%t Denominator/@Convergents[Sqrt[76], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)

%Y Cf. A010528, A041134.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E Formula corrected by _Colin Barker_, Jul 24 2012