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%I #17 Sep 08 2022 08:45:48
%S 2664,20568,68592,161616,314520,542184,859488,1281312,1822536,2498040,
%T 3322704,4311408,5479032,6840456,8410560,10204224,12236328,14521752,
%U 17075376,19912080,23046744,26494248,30269472,34387296,38862600
%N 4*n*(1+45*n+620*n^2).
%C See A167190, where this sequence arises as the integer part of the quotient.
%H Vincenzo Librandi, <a href="/A167191/b167191.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f. 24*x*(111+413*x+96*x^2) / (x-1)^4 . - R. J. Mathar, Jan 27 2012
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jul 02 2012
%t CoefficientList[Series[24*(111+413*x+96*x^2)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 02 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{2664,20568,68592,161616},40] (* _Harvey P. Dale_, Jun 15 2014 *)
%o (Magma) I:=[2664, 20568, 68592, 161616]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 02 2012
%Y Cf. A167190.
%K nonn,easy
%O 1,1
%A _A.K. Devaraj_, Oct 30 2009
%E Extended beyond a(6) by _R. J. Mathar_, Nov 17 2009
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