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A120910 Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is a pair of identical consecutive letters). 1
3, 6, 3, 12, 12, 3, 24, 36, 18, 3, 48, 96, 72, 24, 3, 96, 240, 240, 120, 30, 3, 192, 576, 720, 480, 180, 36, 3, 384, 1344, 2016, 1680, 840, 252, 42, 3, 768, 3072, 5376, 5376, 3360, 1344, 336, 48, 3, 1536, 6912, 13824, 16128, 12096, 6048, 2016, 432, 54, 3, 3072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are the powers of 3 (A000244).

T(n,k) = 3*A038207(n-1,k).

T(n,k) = A120909(n,n-k).

Sum_{k>=0} k*T(n,k) = (n-1)*3^(n-1) = A036290(n-1).

LINKS

Table of n, a(n) for n=1..56.

FORMULA

T(n,k) = 3*2^(n-k-1)*binomial(n-1,k).

G.f.: (1 - (y - 1)*x)/(1 - (y + 2)*x). Generally for the number of length n words with k levels on an m-ary alphabet (m>1): (1 - (y - 1)*x)/(1 - (y + m - 1)*x).  - Geoffrey Critzer, May 19 2014

EXAMPLE

T(3,1)=12 because we have 001,002,011,022,100,110,112,122,200,211,220 and 221.

Triangle starts:

   3;

   6,  3

  12, 12,  3;

  24, 36, 18,  3;

  48, 96, 72, 24,  3;

MAPLE

T:=(n, k)->3*2^(n-k-1)*binomial(n-1, k): for n from 1 to 11 do seq(T(n, k), k=0..n-1) od; # yields sequence in triangular form

MATHEMATICA

sol=Solve[{a==v(z^2+a z), b==v(z^2+b z), c==v(z^2+c z)}, {a, b, c}]; f[z_, u_]:=1/(1-3z-a-b-c)/.sol/.v->u-1; nn=10; Drop[Map[Select[#, #>0&]&, Level[CoefficientList[Series[f[z, u], {z, 0, nn}], {z, u}], {2}]], 1]//Grid (* Geoffrey Critzer, May 19 2014 *)

CROSSREFS

Cf. A000244, A038207, A120909, A036290.

Sequence in context: A337035 A203491 A085709 * A109044 A205844 A205865

Adjacent sequences:  A120907 A120908 A120909 * A120911 A120912 A120913

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Jul 15 2006

STATUS

approved

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Last modified October 28 03:12 EDT 2021. Contains 348308 sequences. (Running on oeis4.)