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%I #4 May 25 2018 11:54:38
%S 0,0,6,72,576,3840,23040,129024,688128,3538944,17694720,86507520,
%T 415236096,1962934272,9160359936,42278584320,193273528320,
%U 876173328384,3942779977728,17626545782784,78340203479040,346346162749440
%N 3n(n-1)4^(n-2).
%C Number of inversions in all 4-ary words of length n on {0,1,2,3}. Example: a(2)=6 because each of the words 10,20,30,21,31,32 has one inversion and the words 00,01,02,03,11,12,13,22,23,33 have no inversions. a(n)=Sum(k*A129531(n,k),k>=0). a(n)=6*A038845(n-2).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).
%F G.f.=6x^2/(1-4x)^3.
%p seq(3*n*(n-1)*4^(n-2),n=0..25);
%t Table[3n(n-1)4^(n-2),{n,0,30}] (* or *) LinearRecurrence[{12,-48,64},{0,0,6},30] (* _Harvey P. Dale_, May 25 2018 *)
%Y Cf. A038845, A129531, A001788, A129530.
%K nonn
%O 0,3
%A _Emeric Deutsch_, Apr 22 2007
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