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A001843
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The coding-theoretic function A(n,4,4).
(Formerly M2644 N1052)
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4
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1, 1, 3, 7, 14, 18, 30, 35, 51, 65, 91, 105, 140, 157, 198, 228, 285, 315, 385, 419, 498, 550, 650, 702, 819, 877, 1005, 1085, 1240, 1320, 1496, 1583, 1773, 1887, 2109, 2223, 2470, 2593, 2856, 3010, 3311, 3465, 3795, 3959, 4308, 4508, 4900, 5100, 5525, 5737
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OFFSET
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4,3
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COMMENTS
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Maximal number of 4-subsets of an n-set such that any two subsets meet in at most 2 points.
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REFERENCES
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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).
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LINKS
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R. K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission]
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1,0,0,1,-1,-1,1,0,0,-1,1,1,-1).
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FORMULA
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See Theorem 1.2 of Bao and Ji, 2015 (Theorem 4.9 in the arXiv preprint, but note the missing parentheses for J(n,4,4) on page 1).
a(n)= +a(n-1) +a(n-2) -a(n-3) +a(n-6) -a(n-7) -a(n-8) +a(n-9) +a(n-12) -a(n-13) -a(n-14) +a(n-15) -a(n-18) +a(n-19) +a(n-20) -a(n-21). - R. J. Mathar, Oct 01 2021
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EXAMPLE
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For n=7 use all seven cyclic shifts of 1110100.
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MAPLE
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floor((n-1)/3* floor((n-2)/2) ) ;
if modp(n, 6) = 0 then
floor(n*(%-1)/4) ;
else
floor(n*%/4) ;
end if;
end proc:
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PROG
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(Python)
[((n-2)//2*(n-1)//3 - int(n%6 == 0)) * n // 4 for n in range(4, 50)]
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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