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A078807
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Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd and first letter 0.
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2
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0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2, 1, 1, 3, 3, 3, 2, 1, 0, 0, 1, 3, 4, 5, 4, 3, 1, 1, 4, 6, 7, 7, 5, 3, 1, 0, 0, 1, 4, 7, 10, 11, 10, 7, 4, 1, 1, 5, 10, 14, 17, 16, 13, 8, 4, 1, 0, 0, 1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1, 1, 6, 15, 25, 35, 40, 39, 32, 22, 12, 5, 1, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Row sums: 0,1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045).
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REFERENCES
| Clark Kimberling, Binary words with restricted repetitions and associated compositions of integers, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 141-151.
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FORMULA
| T(n, k)=T(n-1, n-k-1)+T(n-3, n-k-3)+...+T(n-2m-1, n-k-2m-1), where m=[(n-1)/2] and (by definition) T(i, j)=0 if i<0 or j<0 or i=j.
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EXAMPLE
| T(6,2) counts the words 010001 and 000101. Top of triangle:
0 = T(0,0)
1 = T(1,0)
0 1 = T(2,0) T(2,1)
1 1 0
0 1 1 1
1 2 1 1 0
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CROSSREFS
| Cf. A078808, A078821.
Sequence in context: A113447 A137608 A191336 * A029422 A152800 A117452
Adjacent sequences: A078804 A078805 A078806 * A078808 A078809 A078810
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Dec 07 2002
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