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Search: id:A078821
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| A078821 |
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Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's and all runlengths odd. |
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3
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| 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 1, 0, 2, 4, 4, 4, 2, 0, 1, 3, 4, 5, 5, 4, 3, 1, 0, 2, 6, 8, 10, 8, 6, 2, 0, 1, 4, 7, 10, 12, 12, 10, 7, 4, 1, 0, 2, 8, 14, 20, 22, 20, 14, 8, 2, 0, 1, 5, 11, 18, 25, 29, 29, 25, 18, 11, 5, 1, 0, 2, 10, 22, 36, 48, 52, 48, 36, 22, 10, 2, 0
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows are symmetric. Row sums (0,2,2,4,6,10,16,26,...) are given by 2*F(n), where F(n) is the n-th Fibonacci number, A000045(n).
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REFERENCES
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Clark Kimberling, Binary Words with Restricted Repetitions and Associated Compositions of Integers, preprint.
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FORMULA
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T(n, k)=s(n, k)+t(n, k), where s and t are arrays given by A078807 and A078808.
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EXAMPLE
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T(6,2) counts the words 010001, 000101, 101000 and 100010. Top of triangle:
0 = T(0,0)
1 1 = T(1,0) T(1,1)
0 2 0 = T(2,0) T(2,1) T(2,2)
1 1 1 1
0 2 2 2 0
1 2 2 2 2 1
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CROSSREFS
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Cf. A078807, A078808.
Adjacent sequences: A078818 A078819 A078820 this_sequence A078822 A078823 A078824
Sequence in context: A126205 A025913 A123230 this_sequence A125184 A091430 A059282
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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 07 2002
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