

A005864


The codingtheoretic function A(n,4).
(Formerly M1111)


2



1, 1, 1, 2, 2, 4, 8, 16, 20, 40, 72, 144, 256, 512, 1024, 2048
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OFFSET

1,4


COMMENTS

Since A(n,3) = A(n+1,4), A(n,3) gives essentially the same sequence.
The next term a(17) is in the range 28163276.
Let T_n be the set of SDSmaps of sequential dynamical systems defined over the complete graph K_n in which all vertices have the same vertex function (defined using a set of two possible vertex states). Then a(n) is the maximum number of period2 orbits that a function in T_n can have.  Colin Defant, Sep 15 2015
Since the nhalved cube graph is isomorphic to (or, if you prefer, defined as) the graph with binary sequences of length n1 as nodes and edges between pairs of sequences that differ in at most two positions, the independence number of the nhalved cube graph is A(n1,3) = a(n).  Pontus von BrÃ¶mssen, Dec 12 2018


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 248.
F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, ElsevierNorth Holland, 1978, p. 674.
A. M. Romanov, New binary codes of minimal distance 3, Problemy Peredachi Informatsii, 19 (1983) 101102.
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=1..16.
A. E. Brouwer, Tables of general 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), 13341380.
Colin Defant, Binary Codes and Period2 Orbits of Sequential Dynamical Systems, arXiv:1509.03907 [math.CO], 2015.
Moshe Milshtein, A new binary code of length 16 and minimum distance 3, Information Processing Letters 115.12 (2015): 975976.
P. R. J. Ostergard (patric.ostergard(AT)hut.fi), T. Baicheva and E. Kolev, Optimal binary oneerrorcorrecting codes of length 10 have 72 codewords, IEEE Trans. Inform. Theory, 45 (1999), 12291231.
Eric Weisstein's World of Mathematics, ErrorCorrecting Code
Eric Weisstein's World of Mathematics, Halved Cube Graph
Eric Weisstein's World of Mathematics, Independence Number
Wikipedia, Halved cube graph
Index entries for sequences related to A(n,d)


CROSSREFS

Cf. A005865: A(n,6) ~ A(n,5), A005866: A(n,8) ~ A(n,7).
Cf. A001839: A(n,4,3), A001843: A(n,4,4), A169763: A(n,4,5).
Sequence in context: A279059 A054243 A289670 * A112433 A171648 A189914
Adjacent sequences: A005861 A005862 A005863 * A005865 A005866 A005867


KEYWORD

nonn,hard,nice,more


AUTHOR

N. J. A. Sloane


STATUS

approved



