We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).
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机译：我们得出合理的生成函数，该函数根据与脚在圆盘中心相交的六个生物的组合距离来枚举M. C. Escher的Circle Limit IV中的天使和魔鬼。该结果表明指数增长率的底数为1.582 ...（多项式1的最大根-z ^ 2-2z ^ 3-z ^ 4 + z ^ 6）。
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