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Search: id:A120909
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| A120909 |
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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). |
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+0
2
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| 3, 3, 6, 3, 12, 12, 3, 18, 36, 24, 3, 24, 72, 96, 48, 3, 30, 120, 240, 240, 96, 3, 36, 180, 480, 720, 576, 192, 3, 42, 252, 840, 1680, 2016, 1344, 384, 3, 48, 336, 1344, 3360, 5376, 5376, 3072, 768, 3, 54, 432, 2016, 6048, 12096, 16128, 13824, 6912, 1536, 3, 60
(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*A013609(n-1,k-1). T(n,k)=A120910(n,n-k). Sum(k*T(n,k),k>=1)=3*A081038(n-1).
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FORMULA
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T(n,k)=3*2^(k-1)*binom(n-1,k-1). G(t,z)=3tz/(1-z-2tz).
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EXAMPLE
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T(3,2)=12 because we have 001,002,011,022,100,110,112,122,200,211,220, and 221.
Triangle starts:
3;
3,6;
3,12,12;
3,18,36,24;
3,24,72,96,48;
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MAPLE
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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
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CROSSREFS
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Cf. A000244, A013609, A120910.
Sequence in context: A130695 A058587 A112163 this_sequence A086222 A086492 A051472
Adjacent sequences: A120906 A120907 A120908 this_sequence A120910 A120911 A120912
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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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