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A226882 Number of n-length words w over ternary alphabet {a,b,c} such that #(w,a) >= #(w,b) >= #(w,c) >= 1, where #(w,x) counts the letters x in word w.

%I A226882 #15 Sep 26 2017 15:10:31
%S A226882 6,12,50,180,497,1484,5154,13680,41327,134508,368095,1095367,3521156,
%T A226882 9733564,29025290,92208816,257946527,769203752,2428043309,6848294497,
%U A226882 20442949562,64191187508,182286409175,544512163065,1702858693902,4861764643419,14531465607434
%N A226882 Number of n-length words w over ternary alphabet {a,b,c} such that #(w,a) >= #(w,b) >= #(w,c) >= 1, where #(w,x) counts the letters x in word w.
%H A226882 Alois P. Heinz, <a href="/A226882/b226882.txt">Table of n, a(n) for n = 3..1000</a>
%H A226882 Vaclav Kotesovec, <a href="/A226882/a226882.txt">Recurrence (of order 9)</a>
%F A226882 a(n) ~ 3^n/6 * (1 + 3*sqrt(3/(Pi*n))/2+sqrt(3)*(1+2*cos(2*Pi*n/3))/(Pi*n)). - _Vaclav Kotesovec_, Aug 29 2014
%e A226882 a(4) = 12: aabc, aacb, abac, abca, acab, acba, baac, baca, bcaa, caab, caba, cbaa.
%t A226882 Table[Sum[n!/Product[IntegerPartitions[n,{3}][[k,j]]!,{j,1,3}],{k,1,Length[IntegerPartitions[n,{3}]]}],{n,3,30}] (* _Vaclav Kotesovec_, Aug 29 2014 *)
%Y A226882 Column k=3 of A226874.
%K A226882 nonn
%O A226882 3,1
%A A226882 _Alois P. Heinz_, Jun 21 2013