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Search: id:A065248
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| A065248 |
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Networks with n components. |
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+0
3
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| 0, 4, 3511808, 16417340254783504656, 1461340738496783113671688672284985566897802138624, 3940200619620187981589093886506105584397793947159777
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of special {0,1}^n to {0,1}^n vector-vector maps of which all components are non-neurons, i.e. none is a linearly separable switching function.
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REFERENCES
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Labos E. (1996): Long Cycles and Special Categories of Formal Neuronal Networks. Acta Biologica Hungarica, 47: 261-272.
Labos E. and Sette M.(1995): Long Cycle Generation by McCulloch-Pitts Networks(MCP-Nets) with Dense and Sparse Weight Matrices. Proc. of BPTM, McCulloch Memorial Conference [eds:Moreno-Diaz R. and Mira-Mira J., pp. 350-359.], MIT Press, Cambridge,MA,USA.
McCulloch WS and Pitts W (1943): A Logical Calculus Immanent in Nervous Activity. Bull.Math.Biophys. 5:115-133.
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FORMULA
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a(n)=A064436(n)^n
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EXAMPLE
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For n=2 XOR and its negation are non-neurons, providing 4 networks, all of which permutations are distinguished from each other. For n=3, 152=A064436(3) switching functions are non-neurons, so 152^3=3511808 networks are constructible without formal neurons as component-functions.
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CROSSREFS
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Cf. A000609, A065246, A065247, A064436.
Sequence in context: A046362 A144122 A058424 this_sequence A116141 A067508 A034250
Adjacent sequences: A065245 A065246 A065247 this_sequence A065249 A065250 A065251
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 26 2001
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