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%I #14 Apr 17 2016 03:12:29
%S 1,28,728,18900,490672,12738572,330712200,8585778628,222899532128,
%T 5786802056700,150233953942072,3900296000437172,101257462057424400,
%U 2628793717492597228,68247379192750103528,1771803065294010094500,45998632318451512353472
%N Expansion of (1+2*x+x^2)/(1-26*x+x^2).
%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
%H Vincenzo Librandi, <a href="/A004293/b004293.txt">Table of n, a(n) for n = 0..700</a>
%H J. M. Alonso, <a href="http://dx.doi.org/10.1007/978-1-4612-3142-4_1">Growth functions of amalgams</a>, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (26,-1).
%F From _Colin Barker_, Apr 16 2016: (Start)
%F a(n) = sqrt(7/6)*((13+2*sqrt(42))^(-n)*(-1+(13+2*sqrt(42))^(2*n))) for n>0.
%F a(n) = 26*a(n-1) - a(n-2) for n>2.
%F (End)
%t CoefficientList[Series[(1+2*x+x^2)/(1-26*x+x^2),{x,0,20}],x] (* _Vincenzo Librandi_, Jun 13 2012 *)
%o (PARI) Vec((1+2*x+x^2)/(1-26*x+x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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