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A120909 Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).

%I A120909 #13 Jul 22 2017 02:56:36
%S A120909 3,3,6,3,12,12,3,18,36,24,3,24,72,96,48,3,30,120,240,240,96,3,36,180,
%T A120909 480,720,576,192,3,42,252,840,1680,2016,1344,384,3,48,336,1344,3360,
%U A120909 5376,5376,3072,768,3,54,432,2016,6048,12096,16128,13824,6912,1536,3,60
%N A120909 Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).
%C A120909 Row sums are the powers of 3 (A000244).
%F A120909 T(n,k) = 3*2^(k-1)*binomial(n-1,k-1).
%F A120909 G(t,z) = 3*t*z/(1-z-2*t*z).
%F A120909 T(n,k) = 3*A013609(n-1,k-1).
%F A120909 T(n,k) = A120910(n,n-k).
%F A120909 Sum_{k>=1} k*T(n,k) = 3*A081038(n-1).
%e A120909 T(3,2)=12 because we have 001,002,011,022,100,110,112,122,200,211,220 and 221.
%e A120909 Triangle starts:
%e A120909   3;
%e A120909   3,  6;
%e A120909   3, 12, 12;
%e A120909   3, 18, 36, 24;
%e A120909   3, 24, 72, 96, 48;
%p A120909 T:=(n,k)->3*2^(k-1)*binomial(n-1,k-1): for n from 1 to 11 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form
%t A120909 nn=15;f[list_]:=Select[list,#>0&];a=y x/(1-x) +1;b=a^2/(1-(a-1)^2 );Drop[Map[f,CoefficientList[Series[b a/(1-(a-1)(b-1)),{x,0,nn}],{x,y}]],1]//Grid  (* _Geoffrey Critzer_, Nov 20 2012 *)
%Y A120909 Cf. A000244, A013609, A120910.
%K A120909 nonn,tabl
%O A120909 1,1
%A A120909 _Emeric Deutsch_, Jul 15 2006