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%I #21 Sep 08 2022 08:44:55
%S 1,3,7,17,92,569,2937,6443,15823,53912,2387951,7217765,16823481,
%T 40864727,221147116,1367747423,7059884231,15487515885,38034916001,
%U 129592263888,5740094527073,17349875845107,40439846217287,98229568279681,531587687615692
%N Denominators of continued fraction convergents to sqrt(497).
%H Vincenzo Librandi, <a href="/A041949/b041949.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, 2403774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^18 -3*x^17 +7*x^16 -17*x^15 +92*x^14 -569*x^13 +2937*x^12 -6443*x^11 +15823*x^10 -53912*x^9 -15823*x^8 -6443*x^7 -2937*x^6 -569*x^5 -92*x^4 -17*x^3 -7*x^2 -3*x -1) / (x^20 -2403774*x^10 +1). - _Colin Barker_, Nov 27 2013
%F a(n) = 2403774*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 27 2013
%t Denominator[Convergents[Sqrt[497], 30]] (* _Vincenzo Librandi_, Dec 27 2013 *)
%o (Magma) I:=[1,3,7,17,92,569,2937,6443,15823,53912, 2387951,7217765,16823481,40864727,221147116,1367747423, 7059884231,15487515885,38034916001,129592263888]; [n le 20 select I[n] else 2403774*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2013
%Y Cf. A041948, A040474.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 27 2013
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