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Search: id:A062204
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| A062204 |
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Alignments of a block of n strings of length 7 in a 7n X n array. |
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+0
3
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| 0, 2, 48639, 27684885930, 2428201330563124632, 12374447477223004925451095189, 518707652795611369601687881012709471402, 84188858643128915756437913018700571348711430340961
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Strings of length 7 represent the average word length for most natural languages such as English. This sequence represents the search space for alignment and sequencing algorithms that work on multiple sets of strings.
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REFERENCES
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M. S. Waterman, Introduction to Computational Biology: Maps, Sequences and Genomes, 1995.
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LINKS
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M. A. Covington, The number of distinct alignments of two strings, (pdf, ps), Journal of Quantitative Linguistics, Volume 11, no. 3 (2004), 173-182.
M. S. Waterman, Home Page (contains copies of his papers)
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FORMULA
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A(n, y)= Sum_{k=0, 1, ..., y} ((ny-k)!/(k!((y-k)!)^n)) with y=7.
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EXAMPLE
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A(2,7) = 48639 since this represents the number of unique alignments of 2 strings of length 7. All values in A(2,X) can be cross-validated against the Delannoy sequence D(X,X) A001850.
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CROSSREFS
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Cf. A062205, A062208, A001850. A(2, X) represents Waterman's f function.
Adjacent sequences: A062201 A062202 A062203 this_sequence A062205 A062206 A062207
Sequence in context: A055578 A106025 A094213 this_sequence A059764 A052427 A051833
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KEYWORD
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nonn
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AUTHOR
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Angelo Dalli (adal002(AT)um.edu.mt), Jun 13 2001
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