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A001843 The coding-theoretic function A(n,4,4).
(Formerly M2644 N1052)
2
1, 1, 3, 7, 14, 18, 30, 35, 51, 65, 91, 105, 140, 157, 198, 228, 285, 315, 385 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

COMMENTS

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

The initial known values are 1, 1, 3, 7, 14, 18, 30, 35, 51, 65, 91, 105, 140, 157, 198, 228, 285, 315, 385, 418 or 419, 498, 550, 650, 702, 819, 877, 1005, 1085, 1240, 1320, 1496, >= 1576, ...

The first two open cases are A(23,4,4) >= 418 and A(35,4,4) >= 1576.

REFERENCES

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

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

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

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

LINKS

Table of n, a(n) for n=4..22.

A. E. Brouwer, Bounds for constant weight binary codes

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.

R. K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission]

L. Ji, Asymptotic Determination of the Last Packing Number of Quadruples, Designs, Codes and Cryptography 38 (2006) 83-95.

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

FORMULA

Known exactly for all n except n == 11 mod 12 - see Theorem 5 of Brouwer et al. and Ji.

EXAMPLE

For n=7 use all seven cyclic shifts of 1110100.

CROSSREFS

Sequence in context: A184816 A190700 A267448 * A033808 A161210 A256059

Adjacent sequences:  A001840 A001841 A001842 * A001844 A001845 A001846

KEYWORD

nonn,hard,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Revised by N. J. A. Sloane and Andries E. Brouwer, May 08 2010

STATUS

approved

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Last modified February 23 00:33 EST 2018. Contains 299473 sequences. (Running on oeis4.)