A circular disk is cut into n distinct scctuis. each shaped like a piece of pie and all meeting at the center point of the disk. Each sector is to be painted red. green, yellow, or blue in such a way that no two adjacent sectors arc panned tlx: vainc coJoi. Let .S. be tlie nunibei of ways to paint the disk.
a. Find a recurrence retains Cor Skia terms ofand for each integer 12 4.
b. Find an explicit lor inula for S. for n >2L
(a)
To find the recurrence relation for
Given information:
A circular disk is cut into
Calculation:
Let
Since there are four colors so if suppose one color say red is used for painting the sector, so adjacent sector will be left with
(b)
To find the explicit formula for