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A039754
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Triangle of numbers of inequivalent Boolean functions of n variables with exactly k nonzero values under action of Jevons group.
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4
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1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 6, 3, 3, 1, 1, 1, 1, 4, 6, 19, 27, 50, 56, 74, 56, 50, 27, 19, 6, 4, 1, 1, 1, 1, 5, 10, 47, 131, 472, 1326, 3779, 9013, 19963, 38073, 65664, 98804, 133576, 158658, 169112
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| T(n,k) = number of classes of nonlinear (or linear) binary codes of length n containing k codewords (n>=1, 0 <= k <= 2^n). - Diego Torres (torresvillarroel(AT)hotmail.com), Aug 31 2002
For N=1 through N=5, the first 2^(N-1) terms of row N are also found in triangle A171871, which is related to A005646. This was shown for all N by Andrew Weimholt, Dec 30 2009. [From Robert Munafo (mrob27(AT)gmail.com), Jan 25 2010]
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REFERENCES
| Jacob Feldman, A catalog of Boolean concepts, Journal of Mathematical Psychology, Volume 47, Issue 1, 2003, 75-89.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 112.
M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 150.
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LINKS
| Harald Fripertinger, Enumeration of block codes
Index entries for sequences related to Boolean functions
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FORMULA
| Reference gives g.f.
Fripertinger gives g.f. for the number of classes of (n, m) nonlinear codes over an alphabet of size A.
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EXAMPLE
| 1, 1, 1; 1, 1, 2, 1, 1; 1, 1, 3, 3, 6, 3, 1, 1; ...
Contribution from Robert Munafo (mrob27(AT)gmail.com), Jan 25 2010: (Start)
First 3 rows are:
1, 1, 1
1, 1, 2, 1, 1
1, 1, 3, 3, 6, 3, 3, 1, 1; ...
("1, 1, 1; 1, 1, 2, 1, 1; 1, 1, 3, 3, 6, 3, 1, 1; ..." is in error) (End)
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CROSSREFS
| Row sums give A000616. Cf. A052265.
Cf. A171871 [From Robert Munafo (mrob27(AT)gmail.com), Jan 25 2010]
Sequence in context: A129179 A120621 A201080 * A062277 A204929 A118210
Adjacent sequences: A039751 A039752 A039753 * A039755 A039756 A039757
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KEYWORD
| nonn,tabf,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 20 2000
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