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.

6, 12, 50, 180, 497, 1484, 5154, 13680, 41327, 134508, 368095, 1095367, 3521156, 9733564, 29025290, 92208816, 257946527, 769203752, 2428043309, 6848294497, 20442949562, 64191187508, 182286409175, 544512163065, 1702858693902, 4861764643419, 14531465607434

Offset: 3

Author

Alois P. Heinz, Jun 21 2013

Keywords

• nonn

Examples

			a(4) = 12: aabc, aacb, abac, abca, acab, acba, baac, baca, bcaa, caab, caba, cbaa.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Vaclav Kotesovec, Recurrence (of order 9)

Crossrefs

Column k=3 of A226874.

Programs

Mathematica

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 *)

Formula

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