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%I #19 Jun 30 2023 18:43:49
%S 0,1,8,91,944,10009,105560,1114723,11767904,124240753,1311659432,
%T 13847775787,146197010960,1543466033929,16295047567352,
%U 172033963454899,1816237991957696,19174820948943841,202436993374408520,2137216112616751867
%N a(n) = 8*a(n-1) + 27*a(n-2), with a(0)=0, a(1)=1.
%H Bruno Berselli, <a href="/A190943/b190943.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, 27).
%F G.f.: x/(1-8*x-27*x^2).
%F a(n) = ((4+sqrt(43))^n - (4-sqrt(43))^n)/(2*sqrt(43)).
%t a = {0, 1}; Do[AppendTo[a, 8 a[[-1]] + 27 a[[-2]]], {18}]; a (* _Bruno Berselli_, Dec 26 2012 *)
%t CoefficientList[Series[x / (1 - 8 x - 27 x^2), {x, 0, 25}], x] (* _Vincenzo Librandi_, Aug 19 2013 *)
%o (Maxima) a[0]:0$ a[1]:1$ a[n]:=8*a[n-1]+27*a[n-2]$ makelist(a[n], n, 0, 17);
%o (Magma) [n le 2 select n-1 else 8*Self(n-1)+27*Self(n-2): n in [1..17]];
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-8*x-27*x^2))) \\ _G. C. Greubel_, Dec 30 2017
%Y Cf. A000045, A046717, A015533 (for type of recurrence).
%Y Cf. A015611, A190441 (for type of closed formula).
%K nonn,easy
%O 0,3
%A _Bruno Berselli_, May 24 2011
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