%I #17 Sep 08 2022 08:44:54
%S 1,1,7,22,51,532,1115,3877,24377,28254,589457,617711,4295723,13504880,
%T 31305483,326559710,684424903,2379834419,14963431417,17343265836,
%U 361828748137,379172013973,2636860831975,8289754509898,19216369851771,200453453027608
%N Denominators of continued fraction convergents to sqrt(118).
%H Vincenzo Librandi, <a href="/A041215/b041215.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 (0,0,0,0,0,0,0,0,0,613834,0,0,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^18 -x^17 +7*x^16 -22*x^15 +51*x^14 -532*x^13 +1115*x^12 -3877*x^11 +24377*x^10 -28254*x^9 -24377*x^8 -3877*x^7 -1115*x^6 -532*x^5 -51*x^4 -22*x^3 -7*x^2 -x -1) / (x^20 -613834*x^10 +1). - _Colin Barker_, Nov 14 2013
%F a(n) = 613834*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[118], 30]] (* _Vincenzo Librandi_, Dec 13 2013 *)
%o (Magma) I:=[1, 1, 7, 22, 51, 532, 1115, 3877, 24377, 28254, 589457, 617711, 4295723, 13504880, 31305483, 326559710, 684424903, 2379834419, 14963431417, 17343265836]; [n le 20 select I[n] else 613834*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041214, A010183.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013