# For the second model we need to exclude the case b r

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For the second model, we need to exclude the case b = r = 1 that makes the chain periodic with period 2, and the case b = 1, r = 0, which makes the chain periodic with period + 1. The balance equations are of the form π 1 = (1 b ) π 1 + r ( π (2 , 1) + · · · + π (2 , 1) ) + π (2 , ) , π (2 , 1) = 1 , π (2 ,i ) = (1 r ) π (2 ,i 1) , i = 2 , . . . , . The last two equations can be used to express π (2 ,i ) in terms of π 1 , π (2 ,i ) = (1 r ) i 1 1 , i = 1 , . . . , . 80
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