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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

Table of n, a(n) for n=1..12.

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 * A109903 A249406 A220020

Adjacent sequences:  A152956 A152957 A152958 * A152960 A152961 A152962

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 April 23 23:17 EDT 2017. Contains 285329 sequences.