{"app":{"locale":"en-GB"},"problem":{"content":"

Let $g(n)$ be the number of undirected graphs with $n$ nodes satisfying the following properties:

The graph is connected and has no cycles or multiple edges.
Each node is either red, blue, or yellow.
A red node may have no more than 4 edges connected to it.
A blue or yellow node may have no more than 3 edges connected to it.
An edge may not directly connect a yellow node to a yellow node.

For example, $g(2)=5$, $g(3)=15$, and $g(4) = 57$.
You are also given that $g(10) = 710249$ and $g(100) \\equiv 919747298 \\pmod{1\\,000\\,000\\,007}$.

Find $g(10\\,000) \\bmod 1\\,000\\,000\\,007$.

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