A065248 Networks with n components.

0, 4, 3511808, 16417340254783504656, 1461340738496783113671688672284985566897802138624, 3940200619620187981589093886506105584397793947159777

Offset: 1

Author

Labos Elemer, Oct 26 2001

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A000609, A065246, A065247, A064436.

Formula

a(n)=A064436(n)^n