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 A005864 The coding-theoretic function A(n,4). (Formerly M1111) 2
 1, 1, 1, 2, 2, 4, 8, 16, 20, 40, 72, 144, 256, 512, 1024, 2048 (list; graph; refs; listen; history; text; internal format)
 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 2816-3276. Let T_n be the set of SDS-maps 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 period-2 orbits that a function in T_n can have. - Colin Defant, Sep 15 2015 Since the n-halved cube graph is isomorphic to (or, if you prefer, defined as) the graph with binary sequences of length n-1 as nodes and edges between pairs of sequences that differ in at most two positions, the independence number of the n-halved cube graph is A(n-1,3) = a(n). - Pontus von Brömssen, Dec 12 2018 REFERENCES J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 248. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 674. A. M. Romanov, New binary codes of minimal distance 3, Problemy Peredachi Informatsii, 19 (1983) 101-102. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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), 1334-1380. Colin Defant, Binary Codes and Period-2 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): 975-976. P. R. J. Ostergard (patric.ostergard(AT)hut.fi), T. Baicheva and E. Kolev, Optimal binary one-error-correcting codes of length 10 have 72 codewords, IEEE Trans. Inform. Theory, 45 (1999), 1229-1231. Eric Weisstein's World of Mathematics, Error-Correcting Code Eric Weisstein's World of Mathematics, Halved Cube Graph Eric Weisstein's World of Mathematics, Independence Number Wikipedia, Halved cube graph 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 STATUS approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)