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Problem 867

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Tiling Dodecagon

There are $5$ ways to tile a regular dodecagon of side $1$ with regular polygons of side $1$.

Let $T(n)$ be the number of ways to tile a regular dodecagon of side $n$ with regular polygons of side 1. Then $T(1)=5$. You are also given $T(2)=48$.

Find $T(10)$. Give your answer modulo ${10}^9+7$.

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密铺十二边形

用边长为$1$的正多边形铺满边长为$1$的正十二边形，有$5$种不同的方案：

记$T(n)$为用边长为$1$的正多边形铺满边长为$n$的正十二边形的方案数，因此$T(1)=5$，而$T(2)=48$。

求$T(10)$，并对${10}^9+7$取余作为你的答案。

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