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A001843 The coding-theoretic function A(n,4,4).
(Formerly M2644 N1052)
+0
2
1, 1, 3, 7, 14, 18, 30, 35, 51, 65, 91, 105, 140 (list; graph; listen)
OFFSET

4,3

COMMENT

Maximal number of 4-subsets of an n-set such that any two subsets meet in at most 2 points.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, New table of constant weight codes, IEEE Trans. Info. Theory 36 (1990), 1334-1380.

CRC Handbook of Combinatorial Designs, 1996, p. 411.

R. K. Guy, A problem of Zarankiewicz, in P. Erd\"{o}s and G. Katona, editors, Theory of Graphs (Proceedings of the Colloquium, Tihany, Hungary), Academic Press, NY, 1968, pp. 119-150.

LINKS

E. M. Rains and N. J. A. Sloane, A(n,d,w) tables

Index entries for sequences related to A(n,d,w)

FORMULA

Known exactly for all n except n == 5 mod 6 - see Theorem 5 of Brouwer et al.

EXAMPLE

For n=7 use all cyclic shifts of 11101000.

CROSSREFS

Sequence in context: A128661 A009461 A143630 this_sequence A033808 A161210 A154772

Adjacent sequences: A001840 A001841 A001842 this_sequence A001844 A001845 A001846

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

The first unkown value is a(17), known to be >= 156. It would be nice to settle this case!

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.


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