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Problem #283

Twelve faces of different colors
 Public ★(x6) 02/08/16 by sinan 15xp Math 27.3%

Let there be N distinct colors.

Let an = (an-1 + an-2) % 9 with a1 = a2 = 1

Consider the ways to paint all the faces of dodecahedron using these N distinct colors. If selected, you can use up to ai+2 but no less than 2 of ith color where i = 1 to N.

What is the total number of ways to paint a dodecahedron if N = 1000?

Example: 652706 if N = 5 or 130992447 if N = 10

[My timing: 2s]


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