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%I #21 Jun 13 2015 00:49:22
%S 1,1,4,9,31,40,671,711,2804,6319,21761,28080,471041,499121,1968404,
%T 4435929,15276191,19712120,330670111,350382231,1381816804,3114015839,
%U 10723864321,13837880160,232129946881,245967827041,970033428004,2186034683049,7528137477151
%N Denominators of continued fraction convergents to sqrt(77).
%H Vincenzo Librandi, <a href="/A041137/b041137.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 (0,0,0,0,0,702,0,0,0,0,0,-1).
%F a(n) = 702*a(n-6)-a(n-12). G.f.: -(x^10-x^9+4*x^8-9*x^7+31*x^6-40*x^5-31*x^4-9*x^3-4*x^2-x-1)/((x^4-9*x^2+1)*(x^8+9*x^6+80*x^4+9*x^2+1)). [_Colin Barker_, Jul 18 2012]
%t Denominator/@Convergents[Sqrt[77], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)
%t CoefficientList[Series[- (x^10 - x^9 + 4 x^8 - 9 x^7 + 31 x^6 - 40 x^5 - 31 x^4 - 9 x^3 - 4 x^2 - x - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 24 2013 *)
%Y Cf. A010529, A041136.
%K nonn,cofr,frac,easy
%O 0,3
%A _N. J. A. Sloane_.