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A000609 Number of threshold functions of n or fewer variables.
(Formerly M1285 N0492)
2, 4, 14, 104, 1882, 94572, 15028134, 8378070864, 17561539552946, 144130531453121108 (list; graph; refs; listen; history; text; internal format)



Gruzling, Nicolle, Linear separability of the vertices of an n-dimensional hypercube. M.Sc Thesis. University of Northern British Columbia, 2006. [From W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010]

Sze-Tsen Hu, Threshold Logic, University of California Press, 1965 see page 57.

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 3.

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825.

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).

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

C. Stenson, Weighted voting, threshold functions, and zonotopes, in The Mathematics of Decisions, Elections, and Games, Volume 625 of Contemporary Mathematics Editors  Karl-Dieter Crisman, Michael A. Jones, American Mathematical Society, 2014, ISBN 0821898663, 9780821898666

R. O. Winder, Threshold Logic, Doctoral Dissertation, Math. Dept., Princeton University, May 1962.

R. O. Winder, Enumeration of seven-argument threshold functions, IEEE Trans. Electron. Computers, 14 (1965), 315-325.


Wang Lan, Table of n, a(n) for n = 0..9 [This replaces an earlier b-file computed by David Wasserman]

Guido F. Montufar and Jason Morton, When Does a Mixture of Products Contain a Product of Mixtures?,  arXiv preprint arXiv:1206.0387, 2012.

S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]

Muroga, Saburo, Iwao Toda, and Satoru Takasu, Theory of majority decision elements, Journal of the Franklin Institute 271.5 (1961): 376-418. [Annotated scans of pages 413 and 414 only]

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]

Stephen Wolfram, A New Kind Of Science. page 1102.

Wikipedia, Linear separability [From W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010]

Index entries for "core" sequences

Index entries for sequences related to Boolean functions


Cf. A000615, A109456, A116986.

Sequence in context: A032052 A005737 A219767 * A245079 A167008 A238638

Adjacent sequences:  A000606 A000607 A000608 * A000610 A000611 A000612




N. J. A. Sloane


One more term from W. Lan (wl(AT)fjrtvu.edu.cn), Jun 27 2010



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Last modified July 26 04:32 EDT 2017. Contains 289798 sequences.