Search: id:A001206
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%I A001206 M1267 N0486
%S A001206 0,1,2,4,12,81,2646,1422564,229809982112
%N A001206 Number of self-dual monotone Boolean functions of n variables.
%C A001206 Sometimes called Hosten-Morris numbers.
%C A001206 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
%C A001206 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
%C A001206 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
%C A001206 Also the number of nondominated coteries on n members. - D. E. Knuth 
               Sep 01 2005
%C A001206 The number of maximal families of intersecting subsets of an n element 
               set. - Bridget Eileen Tenner (bridget(AT)math.mit.edu), Nov 16 2006
%D A001206 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001206 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001206 Jan C. Bioch and Toshihide Ibaraki, Generating and approximating nondominated 
               coteries, IEEE Transactions on parallel and distributed systems, 
               6 (1995), 905-914.
%D A001206 Hosten, Serkan and Morris, Walter D., Jr., The order dimension of the 
               complete graph, Discrete Math. 201 (1999), 133-139.
%D A001206 Jovovic V. and Kilibarda G., The number of n-variable Boolean functions 
               in the Post class F(7,2), Belgrade, 2001, in preparation.
%D A001206 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4, 
               in preparation.
%D A001206 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.
%D A001206 E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Springer, 
               2005.
%H A001206 D. E. Loeb, <a href="http://www.labri.u-bordeaux.fr/~loeb/london">Challenges 
               in playing multiplayer games</a>, in Levy and Beal, editors, Heuristic 
               Programming in Artificial Intelligence, vol. 4, Ellis Horwood, 1994.
%H A001206 D. E. Loeb and A. Meyerowitz, <a href="http://www.labri.u-bordeaux.fr/
               ~loeb/nov94">The maximal intersecting family of sets graph</a>, in 
               H. Barcelo and G. Kalai, editors, Proceedings of the Conference on 
               Jerusalem Combinatorics 1993. AMS series Contemporary Mathematics, 
               1994.
%H A001206 <a href="Sindx_Bo.html#Boolean">Index entries for sequences related to 
               Boolean functions</a>
%F A001206 a(n+1)=Sum_{m=0..A037952(n)} A059090(n, m).
%e A001206 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.
%Y A001206 Cf. A059090, A000372.
%Y A001206 Sequence in context: A038054 A003180 A002080 this_sequence A144295 A119489 
               A053631
%Y A001206 Adjacent sequences: A001203 A001204 A001205 this_sequence A001207 A001208 
               A001209
%K A001206 nonn,hard,nice
%O A001206 0,3
%A A001206 N. J. A. Sloane (njas(AT)research.att.com).
%E A001206 a(8) from Daniel Loeb, daniel.loeb(AT)verizon.net, Jan 04 1996.
%E A001206 a(8) confirmed by D. E. Knuth, Feb 08 2008

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