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Search: id:A078803
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| A078803 |
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Triangular array T given by T(n,k)= number of compositions of n into k parts, each in the set {1,2,3}. |
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2
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| 1, 1, 1, 1, 2, 1, 0, 3, 3, 1, 0, 2, 6, 4, 1, 0, 1, 7, 10, 5, 1, 0, 0, 6, 16, 15, 6, 1, 0, 0, 3, 19, 30, 21, 7, 1, 0, 0, 1, 16, 45, 50, 28, 8, 1, 0, 0, 0, 10, 51, 90, 77, 36, 9, 1, 0, 0, 0, 4, 45, 126, 161, 112, 45, 10, 1, 0, 0, 0, 1, 30, 141, 266, 266, 156, 55, 11, 1, 0, 0, 0, 0, 15, 126
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Reversing the rows produces A078802. Row sums: A000073.
Number of tribonacci binary words of length n-1 having k-1 1's. A tribonacci binary word is a binary word having no three consecutive 0's. Example: T(6,3)=7 because we have 00101,00110,01001,01010,01100,10010 and 10100. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 16 2007
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REFERENCES
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C. Kimberling, Binary Words with Restricted Repetitions and Associated Compositions of Integers, preprint.
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FORMULA
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T(n, k)=t(n-1, n-k), for 1<=k<=n, for n>=1, where array t is given by A078802.
G.f.: 1/[1-tz(1+z+z^2)]-1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 10 2004
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EXAMPLE
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T(5,2)=2 counts the compositions 2+3 and 3+2. Top of triangle T:
1
1 1
1 2 1
0 3 3 1
0 2 6 4 1
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CROSSREFS
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Cf. A027907, A078802.
Sequence in context: A072661 A103432 A103448 this_sequence A130403 A130402 A089840
Adjacent sequences: A078800 A078801 A078802 this_sequence A078804 A078805 A078806
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Dec 06 2002
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 16 2007
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