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Search: id:A120910
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| A120910 |
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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). |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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*T(n,k),k>=0)=(n-1)*3^(n-1)=A036290(n-1).
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FORMULA
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T(n,k)=3*2^(n-k-1)*binom(n-1,k).
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EXAMPLE
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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;
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MAPLE
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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
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CROSSREFS
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Cf. A000244, A038207, A120909, A036290.
Sequence in context: A128503 A120906 A085709 this_sequence A109044 A085881 A127574
Adjacent sequences: A120907 A120908 A120909 this_sequence A120911 A120912 A120913
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2006
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