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%I #18 Sep 08 2022 08:44:53
%S 1,1,2,7,37,118,155,273,2885,3158,6043,21287,112478,358721,471199,
%T 829920,8770399,9600319,18370718,64712473,341933083,1090511722,
%U 1432444805,2522956527,26662010075,29184966602,55846976677,196725896633,1039476459842,3315155276159
%N Denominators of continued fraction convergents to sqrt(31).
%H Vincenzo Librandi, <a href="/A041051/b041051.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 (0,0,0,0,0,0,0,3040,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +37*x^10 -118*x^9 +155*x^8 -273*x^7 -155*x^6 -118*x^5 -37*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -3040*x^8 +1). - _Colin Barker_, Nov 12 2013
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[31],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011*)
%t Denominator[Convergents[Sqrt[31], 30]] (* _Vincenzo Librandi_, Dec 10 2013 *)
%o (Magma) I:=[1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920]; [n le 16 select I[n] else 3040*Self(n-8) - Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 10 2013
%Y Cf. A041050, A010129, A020788, A010486.
%K nonn,cofr,easy,frac
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 12 2013
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