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%I #16 Sep 08 2022 08:45:10
%S 1,4,10,28,84,260,812,2532,7852,24196,74124,225956,686060,2076612,
%T 6270796,18902500,56904108,171138308,514332428,1544963364,4639084396,
%U 13926166084,41797372620,125431963748,376379777324,1129315492740
%N a(n) = 4*3^n/3 - 5*0^n/6 - (n-1)2^(n-1).
%H Harvey P. Dale, <a href="/A083587/b083587.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-16,12).
%F G.f.: (-10*x^3+2*x^2+3*x-1)/((2*x-1)^2*(3*x-1)). - _Harvey P. Dale_, Dec 31 2014
%t Join[{1},LinearRecurrence[{7,-16,12},{4,10,28},30]] (* _Harvey P. Dale_, Dec 31 2014 *)
%t Join[{1}, Table[4 3^n / 3 - 5 0^n / 6 - (n-1) 2^(n-1), {n, 1, 40}]] (* _Vincenzo Librandi_, Jan 01 2015 *)
%o (Magma) [4*3^n/3-5*0^n/6-(n-1)*2^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jan 01 2015
%Y Cf. A083588.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 01 2003