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%I #17 Sep 08 2022 08:45:30
%S 6,108,972,6480,36450,183708,857304,3779136,15943230,64953900,
%T 257217444,994857552,3772168218,14061928860,51656065200,187339329792,
%U 671787127926,2384960530284,8391527791740,29288988968400,101486346775506
%N (n^3+n^2)*3^n.
%H Vincenzo Librandi, <a href="/A129003/b129003.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (12,-54,108,-81).
%F G.f.: 6x(1+6x)/(1-3x)^4. [From _R. J. Mathar_, Dec 19 2008]
%F a(n) = 12*a(n-1)-54*a(n-2)+108*a(n-3)-81*a(n-4). - _Vincenzo Librandi_, Feb 12 2013
%F a(n) = 6*(A036216(n-1)+6*A036216(n-2)), with A036216(-1)=0. [_Bruno Berselli_, Feb 12 2013]
%t LinearRecurrence[{12, -54, 108, -81}, {6, 108, 972, 6480}, 30] (* _Vincenzo Librandi_, Feb 12 2013 *)
%o (Magma) [(n^3+n^2)*3^n: n in [1..25]]; /* or */ I:=[6,108,972,6480]; [n le 4 select I[n] else 12*Self(n-1)-54*Self(n-2)+108*Self(n-3)-81*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%Y Cf. A036216, A128796, A036289.
%K nonn,easy
%O 1,1
%A _Mohammad K. Azarian_, May 01 2007
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