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$Old$ November 3rd, 2009, 11:51 AM

ilovebillu $ilovebillu is offline$

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$Default$ problem in recursion

A circular disk is cut into n distinct sectors, each shaped like a piece of pie and all meeting at the centre point of the disk. Each sector is to be painted red, green, yellow, or blue in such a way that no two adjacent sectors are painted the same color. Let Sn be the number of ways to paint the disk.
(i) Find a recurrence relation for Sn.
(ii) Solve the recurrence relation.
(Note: It is a circular disk, so the start sector and the end sector are adjacent.)

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