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%I #16 Sep 08 2022 08:44:54
%S 1,1,3,4,7,18,25,868,893,2654,3547,6201,15949,22150,769049,791199,
%T 2351447,3142646,5494093,14130832,19624925,681378282,701003207,
%U 2083384696,2784387903,4867772599,12519933101,17387705700,603701926901,621089632601,1845881192103
%N Denominators of continued fraction convergents to sqrt(314).
%H Vincenzo Librandi, <a href="/A041593/b041593.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 (0,0,0,0,0,0,886,0,0,0,0,0,0,1).
%F G.f.: -(x^12-x^11+3*x^10-4*x^9+7*x^8-18*x^7+25*x^6+18*x^5+7*x^4+4*x^3+3*x^2+x+1) / (x^14+886*x^7-1). - _Colin Barker_, Nov 19 2013
%F a(n) = 886*a(n-7) + a(n-14) for n>13. - _Vincenzo Librandi_, Dec 21 2013
%t Denominator[Convergents[Sqrt[314], 30]] (* _Harvey P. Dale_, Aug 08 2013 *)
%t CoefficientList[Series[-(x^12 - x^11 + 3 x^10 - 4 x^9 + 7 x^8 - 18 x^7 + 25 x^6 + 18 x^5 + 7 x^4 + 4 x^3 + 3 x^2 + x + 1)/(x^14 + 886 x^7 - 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 21 2013 *)
%o (Magma) I:=[1,1,3,4,7,18,25,868,893,2654,3547,6201, 15949,22150]; [n le 14 select I[n] else 886*Self(n-7)+Self(n-14): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2013
%Y Cf. A041592, A040296.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 19 2013