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%I #34 Feb 23 2022 09:46:45
%S 1,6,24,84,276,876,2724,8364,25476,77196,233124,702444,2113476,
%T 6352716,19082724,57297324,171990276,516167436,1548895524,4647473004,
%U 13943991876,41835121356,125511655524,376547549484,1129667814276
%N a(n) = 4*3^n - 3*2^n.
%C Second binomial transform of A123932 = [1,4,4,4,4,4,4,4,...].
%H Vincenzo Librandi, <a href="/A166060/b166060.txt">Table of n, a(n) for n = 0..1000</a>
%H John Elias, <a href="/A166060/a166060.png">Illustration of initial terms: Sierpinski-tetra-triangles</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6).
%F a(n) = 5*a(n-1) - 6*a(n-2) for n > 1; a(0)= 1, a(1)= 6.
%F G.f.: (1+x)/(1-5x+6x^2).
%F a(n) = A217764(n,6). - _Ross La Haye_, Mar 27 2013
%F a(n) = Sum_{k = 1..2^n} A082560(n+1,k). - _Reinhard Zumkeller_, May 14 2015
%t CoefficientList[Series[(1+x)/((1-2x)*(1-3x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05 2012 *)
%o (PARI) a(n)=4*3^n-3<<n \\ _Charles R Greathouse IV_, Jan 12 2012
%o (Magma) [4*3^n-3*2^n: n in [0..30]]; // _Vincenzo Librandi_, Dec 05 2012
%o (Haskell)
%o a166060 n = a166060_list !! n
%o a166060_list = map fst $ iterate (\(u, v) -> (3 * (u + v), 2 * v)) (1, 1)
%o -- _Reinhard Zumkeller_, Jun 09 2013
%Y Cf. A082560, A123932, A257956.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Oct 05 2009
%E a(19) and a(22) corrected by _Charles R Greathouse IV_, Jan 12 2012
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