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%I #30 Feb 05 2022 16:08:01
%S 1,1,2,3,14,17,31,48,223,271,494,765,3554,4319,7873,12192,56641,68833,
%T 125474,194307,902702,1097009,1999711,3096720,14386591,17483311,
%U 31869902,49353213,229282754,278635967
%N Denominators of continued fraction convergents to sqrt(7).
%C Sqrt(7) = 2 + 9/14 + 9/(14*223) + 9/(223*3554) + 9/(3554*56641) + ...; sum of these 5 terms = 2.64575131088, with sqrt(7) = 2.64575131106... The terms 14, 223, 3554, ... = a(4), a(8), a(12), ... - _Gary W. Adamson_, Dec 27 2007
%H Vincenzo Librandi, <a href="/A041009/b041009.txt">Table of n, a(n) for n = 0..1000</a>
%H C. Elsner, M. Stein, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Elsner2/elsner10.html">On Error Sum Functions Formed by Convergents of Real Numbers</a>, J. Int. Seq. 14 (2011) # 11.8.6
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,16,0,0,0,-1).
%F G.f.: (1+x+2*x^2+3*x^3-2*x^4+x^5-x^6)/(1-16*x^4+x^8). - _Colin Barker_, Mar 13 2012
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[7],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2011*)
%t Denominator[Convergents[Sqrt[7],30]] (* or *) LinearRecurrence[ {0,0,0,16,0,0,0,-1},{1,1,2,3,14,17,31,48},30] (* _Harvey P. Dale_, Dec 17 2019 *)
%Y Cf. A010465, A041008.
%K nonn,cofr,frac,easy
%O 0,3
%A _N. J. A. Sloane_