%I #13 Jul 31 2015 17:14:39
%S 4,17,65,244,912,3405,12709,47432,177020,660649,2465577,9201660,
%T 34341064,128162597,478309325,1785074704,6661989492,24862883265,
%U 92789543569,346295291012,1292391620480,4823271190909,18000693143157
%N a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -5, 1).
%F G.f.: (3x-4)/((x-1)(x^2-4x+1))
%F (1/2) [A001353(n+1) + 5*A001353(n) - 1 ]. - _Ralf Stephan_, May 17 2007
%F a(n)=1/12*((3-7*Sqrt[3])*(2-Sqrt[3])^n+(3+7*Sqrt[3])*(2+Sqrt[3])^n-6). - _Harvey P. Dale_, Mar 15 2013
%t a[0] = 4; a[1] = 17; a[2] = 65; a[n_] := a[n] = 5a[n - 1] - 5a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 22}] (* Or *)
%t CoefficientList[ Series[(3x - 4)/((x - 1)(x^2 - 4x + 1)), {x, 0, 22}], x] (* _Robert G. Wilson v_, Jan 12 2005 *)
%t LinearRecurrence[{5,-5,1},{4,17,65},30] (* or *) With[{c=Sqrt[3]},Table[ Simplify[ ((3-7c)(2-c)^x+(2+c)^x (3+7c)-6)/12],{x,30}]] (* _Harvey P. Dale_, Mar 15 2013 *)
%Y Cf. A061278, A092184, A001834, A001353, A102206.
%K nonn
%O 0,1
%A _Creighton Dement_, Dec 30 2004
%E More terms from _Robert G. Wilson v_, Jan 12 2005