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A001206
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Number of self-dual monotone Boolean functions of n variables.
(Formerly M1267 N0486)
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7
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OFFSET
| 0,3
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COMMENTS
| Sometimes called Hosten-Morris numbers.
Also the number of simplicial complexes on the set {1, ..., n-1} such that no pair of faces covers all of {1, ..., n-1}. [Miller-Sturmfels]. - N. J. A. Sloane (njas(AT)research.att.com), Feb 18 2008
Also the maximal number of generators of a neighborly monomial ideal in n variables. [Miller-Sturmfels]. - N. J. A. Sloane (njas(AT)research.att.com), Feb 18 2008
Also the number of intersecting antichains on a labeled (n-1)-set or (n-1)-variable Boolean functions in the Post class F(7,2). Cf. A059090. - Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Dec 28 2000
Also the number of nondominated coteries on n members. - D. E. Knuth Sep 01 2005
The number of maximal families of intersecting subsets of an n element set. - Bridget Eileen Tenner (bridget(AT)math.mit.edu), Nov 16 2006
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REFERENCES
| Jan C. Bioch and Toshihide Ibaraki, Generating and approximating nondominated coteries, IEEE Transactions on parallel and distributed systems, 6 (1995), 905-914.
Hosten, Serkan and Morris, Walter D., Jr., The order dimension of the complete graph, Discrete Math. 201 (1999), 133-139.
Jovovic V. and Kilibarda G., The number of n-variable Boolean functions in the Post class F(7,2), Belgrade, 2001, in preparation.
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
W. F. Lunnon, The IU function: the size of a free distributive lattice, pp. 173-181 of D. J. A. Welsh, editor, Combinatorial Mathematics and Its Applications. Academic Press, NY, 1971.
E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Springer, 2005.
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
| D. E. Loeb, Challenges in playing multiplayer games, in Levy and Beal, editors, Heuristic Programming in Artificial Intelligence, vol. 4, Ellis Horwood, 1994.
D. E. Loeb and A. Meyerowitz, The maximal intersecting family of sets graph, in H. Barcelo and G. Kalai, editors, Proceedings of the Conference on Jerusalem Combinatorics 1993. AMS series Contemporary Mathematics, 1994.
Index entries for sequences related to Boolean functions
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FORMULA
| a(n+1)=Sum_{m=0..A037952(n)} A059090(n, m).
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EXAMPLE
| a(2) = 1 + 1 = 2; a(3) = 1 + 3 = 4; a(4) = 1 + 7 + 3 + 1 = 12; a(5) = 1 + 15 + 30 + 30 + 5 = 81; a(6) = 1 + 31 + 195 + 605 + 780 + 543 + 300 + 135 + 45 + 10 + 1 = 2646; a(7) = 1 + 63 + 1050 + 9030 + 41545 + 118629 + 233821 + 329205 + 327915 + 224280 + 100716 + 29337 + 5950 + 910 + 105 + 1 = 1422564. Cf. A059090.
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CROSSREFS
| Cf. A059090, A000372.
Sequence in context: A038054 A003180 A002080 * A144295 A119489 A053631
Adjacent sequences: A001203 A001204 A001205 * A001207 A001208 A001209
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KEYWORD
| nonn,hard,nice,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(8) from Daniel Loeb, daniel.loeb(AT)verizon.net, Jan 04 1996.
a(8) confirmed by D. E. Knuth, Feb 08 2008
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