A065248 Networks with n components.

0, 4, 3511808, 16417340254783504656, 1461340738496783113671688672284985566897802138624, 3940200619620187981589093886506105584397793947159777

Offset

1,2

Comments

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.

References

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.

Links

Table of n, a(n) for n=1..6.

Formula

a(n)=A064436(n)^n

Example

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.

Crossrefs

Cf. A000609, A065246, A065247, A064436.

Sequence in context: A144122 A058424 A204041 * A116141 A225876 A067508

Adjacent sequences: A065245 A065246 A065247 * A065249 A065250 A065251

Keyword

nonn

Author

Labos Elemer, Oct 26 2001

Status

approved