0,3

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.

The assertion that "strings of length 7 represent the average word length for most natural languages such as English" seems to conflict with studies that show that the average word length in English is about 4.5 letters and the average word length in modern Russian is 5.28 letters. - M. F. Hasler, Mar 12 2009

M. S. Waterman, Introduction to Computational Biology: Maps, Sequences and Genomes, 1995.

M. A. Covington, The number of distinct alignments of two strings, Journal of Quantitative Linguistics, Volume 11, no. 3 (2004), 173-182. [Link corrected by Ray Chandler, Mar 12 2009]

Michael S. Waterman, Home Page (contains copies of his papers) [Link corrected by R. J. Mathar, Mar 11, 2009]

A(n, y) = sum(k=0,n*y, sum(t=0,k, (-1)^t * binomial(k,t) * binomial(k-t,y)^n ))

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.

Cf. A062205, A062208, A001850. A(2, X) represents Waterman's f function.

Sequence in context: A024761 A140924 A048341 this_sequence A067869 A157667 A061737

Adjacent sequences: A062201 A062202 A062203 this_sequence A062205 A062206 A062207

nonn

Angelo Dalli (adal002(AT)um.edu.mt) [broken email address], Jun 13 2001

Formula and sequence revised by Max Alekseyev, Mar 12 2009