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A001843 The coding-theoretic function A(n,4,4).
(Formerly M2644 N1052)
4
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 (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.
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
Jingjun Bao and Lijun Ji, The completion determination of optimal (3,4)-packings, Des. Codes Cryptogr. 77, 217-229 (2015); arXiv:1401.2022 [math.CO], 2014.
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 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).
FORMULA
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
EXAMPLE
For n=7 use all seven cyclic shifts of 1110100.
MAPLE
A001843 := proc(n)
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:
seq(A001843(n), n=4..80) ; # R. J. Mathar, Oct 01 2021
PROG
(Python)
[((n-2)//2*(n-1)//3 - int(n%6 == 0)) * n // 4 for n in range(4, 50)]
# Andrey Zabolotskiy, Jan 28 2021
CROSSREFS
Sequence in context: A310268 A190700 A267448 * A310269 A033808 A310270
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Revised by N. J. A. Sloane and Andries E. Brouwer, May 08 2010
Terms a(23) and beyond added, entry edited by Andrey Zabolotskiy, Jan 28 2021
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)