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%I #16 Sep 08 2022 08:44:54
%S 1,1,5,16,53,228,281,8658,8939,44414,142181,470957,2026009,2496966,
%T 76934989,79431955,394662809,1263420382,4184923955,18003116202,
%U 22188040157,683644320912,705832361069,3506973765188,11226753656633,37187234735087,159975692596981
%N Denominators of continued fraction convergents to sqrt(250).
%H Vincenzo Librandi, <a href="/A041469/b041469.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 (0,0,0,0,0,0,8886,0,0,0,0,0,0,1).
%F G.f.: -(x^12 -x^11 +5*x^10 -16*x^9 +53*x^8 -228*x^7 +281*x^6 +228*x^5 +53*x^4 +16*x^3 +5*x^2 +x +1) / (x^14 +8886*x^7 -1). - _Colin Barker_, Nov 18 2013
%F a(n) = 8886*a(n-7) + a(n-14) for n>13. - _Vincenzo Librandi_, Dec 18 2013
%t Denominator[Convergents[Sqrt[250], 30]] (* _Vincenzo Librandi_, Dec 18 2013 *)
%o (Magma) I:=[1,1,5,16,53,228,281,8658,8939,44414,142181, 470957,2026009,2496966]; [n le 14 select I[n] else 8886*Self(n-7)+Self(n-14): n in [1..40]]; // _Vincenzo Librandi_, Dec 18 2013
%Y Cf. A041468, A040234.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 18 2013
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