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A152959 Number of correlation classes for pairs of different words in an alphabet of size 4. 0
1, 6, 20, 55, 141, 324, 657, 1329, 2515, 4592, 7897, 13221 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let b(m,q) be the number of correlation classes of pairs of different q-ary words of length m, per the definition of sequence A152139. Then here a(m)=b(m,4), the number of correlation classes of pairs of different words of length m in an alphabet of size 4. In other words, for m>1, a(m)=c(m*(m-1)+4), where c is given by A152139. A conjecture mentioned in the comments to A152139 translates here to b(m,q) = a(m) for all q > 4. For more details, see the comments in A152139.
REFERENCES
Leo J. Guibas and Andrew M. Odlyzko, String overlaps, pattern matching and nontransitive games, Journal of Combinatorial Theory Series A, 30 (1981), 183-208.
Sven Rahmann and Eric Rivals, On the distribution of the number of missing words in random texts, Combinatorics, Probability and Computing (2003) 12, 73-87.
Andrew L. Rukhin, Distribution of the number of words with a prescribed frequency and tests of randomness, Advances in Probability, Vol. 34, No. 4, (Dec 2002), 775-797.
LINKS
EXAMPLE
Rahmann and Rivals [Table 1] has a(2)=6.
CROSSREFS
Cf. A152139. See also A005434, which treats autocorrelations.
Sequence in context: A028492 A059822 A213589 * A328681 A109903 A323640
KEYWORD
hard,more,nonn
AUTHOR
Paul Leopardi, Dec 15 2008, Dec 28 2008
EXTENSIONS
a(11)=7897, a(12)=13221 added by Paul Leopardi, Apr 20 2010
STATUS
approved

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Last modified March 19 02:46 EDT 2024. Contains 370952 sequences. (Running on oeis4.)