Problem 194

Coloured Configurations

Consider graphs built with the units A: and B: , where the units are glued along the vertical edges as in the graph .

A configuration of type (`a`,`b`,`c`) is a graph thus built of `a` units A and `b` units B, where the graph's vertices are coloured using up to `c` colours, so that no two adjacent vertices have the same colour.

The compound graph above is an example of a configuration of type (2,2,6), in fact of type (2,2,`c`) for all `c` 4.

Let N(`a`,`b`,`c`) be the number of configurations of type (`a`,`b`,`c`).

For example, N(1,0,3) = 24, N(0,2,4) = 92928 and N(2,2,3) = 20736.

Find the last 8 digits of N(25,75,1984).

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