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%I #14 Sep 08 2022 08:45:11
%S 1,4,14,48,166,584,2094,7648,28406,107064,408574,1575248,6123846,
%T 23963944,94261454,372262848,1474702486,5855763224,23293912734,
%U 92788230448,369990660326,1476475856904,5895443074414,23550391238048
%N Expansion of (1-4x+x^2)/((1-x)(1-3x)(1-4x)).
%C Binomial transform of A085279.
%H Vincenzo Librandi, <a href="/A085280/b085280.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).
%F a(n) = 3^n+4^n/3-1/3.
%t Table[(3^n + 4^n/3 - 1/3), {n, 0, 30}] (* _Vincenzo Librandi_, May 26 2013 *)
%t CoefficientList[Series[(1-4x+x^2)/((1-x)(1-3x)(1-4x)),{x,0,30}],x] (* _Harvey P. Dale_, Jan 02 2021 *)
%o (Magma) [3^n+4^n/3-1/3: n in [0..30]]; // _Vincenzo Librandi_, May 26 2013
%K nonn,easy
%O 0,2
%A _Paul Barry_, Jun 25 2003
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