Consider walks in the X Y plane where each step is R (x,y)(x 1, y) or...

Consider walks in the X-Y plane where each step is R: (x, y)â†’(x+1, y) or U:...

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Advance Math

Consider walks in the X-Y plane where each step is R: (x,y)â†’(x+1, y) or U: (x, y)â†’(x, y+a), with a a positive integer. Thereare five walks that contain a point on the line x + y = 2,namely:Â Â RR, RU1, U1R, U1U1, and U2. Let a_n denote thenumber of walks that contain a point on the line x + y = n (so a_2= 5). Show that a_n = F_{2n}, where F_n are the Fibonacci numbersstarting with F_0 = F_1 = 1.

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Here we have to show that anFF2 PROOF Suppose Wn is the set of walks that contain a point on the line given by following equation x y n For X R U and also let Wn X be the set of walks that contain a point on the line x y n and start with X Now We may extend a walk w Wn1 to a walk in Wn that See Answer

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