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%I #32 Dec 22 2020 18:29:00
%S 1,12,120,1188,11760,116412,1152360,11407188,112919520,1117788012,
%T 11064960600,109531817988,1084253219280,10733000374812,
%U 106245750528840,1051724504913588,10410999298607040,103058268481156812,1020171685512961080,10098658586648453988
%N Expansion of (1 + 2*x + x^2)/(1 - 10*x + x^2).
%D J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.
%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
%H Vincenzo Librandi, <a href="/A004291/b004291.txt">Table of n, a(n) for n = 0..1000</a>
%H Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-1).
%F a(n) = 12*A004189(n), n> 0. - _R. J. Mathar_, Oct 29 2012
%F a(n) = sqrt(3/2)*(-(5 - 2*sqrt(6))^n + (5 + 2*sqrt(6))^n) for n > 0. - _Colin Barker_, Jan 25 2016
%F For n > 0: a(n) = 10*a(n-1) - a(n-2) with a(0) = 0, a(1) = 12. - _A.H.M. Smeets_, Jul 25 2017
%t CoefficientList[Series[(1+2*x+x^2)/(1-10*x+x^2),{x,0,30}],x] (* _Vincenzo Librandi_, Jun 13 2012 *)
%o (PARI) Vec((1+2*x+x^2)/(1-10*x+x^2) + O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Pairwise sums of A054320.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_