15. Use generating functions to solve the recurrence equation rn = rn-1 + 6rn-2 for n...
Applied combinatorics.
17. Let bo 1, b2 = 1, and b-4. Use generating functions to solve the recurrence equation bn+3-4bn+2 -bnt1 6bn 3n forn20.
17. Let bo 1, b2 = 1, and b-4. Use generating functions to solve the recurrence equation bn+3-4bn+2 -bnt1 6bn 3n forn20.
1) Use Generating Functions to solve each of the following recurrence relations: (a) a(n)=2a(n-1)-a(n-2) if n>1, while a(0)=2, a(1)=1
Use generating functions to solve the following recurrence. T(0) = 0, T(1) = 1. T(n) = 7 T(n-1) – 12 T(n-2)
(1 point) Find the solution to the following lhcc recurrence: lan-1 + 20an-2 for n > 2 with initial conditions do = 2, a1 = 5. The solution is of the form: an = An = ai(rı)” + az(r2)" for suitable constants Q1, Q2, r1, r2 with rı = r2. Find these constants. r2 = ri = a = A2 =
6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
Solve the following recurrence relation together with initial condition, by any method an = an-1 + 2n, n > 2, ai = 6
For these recurrence relations, solve for general equation using
characteristics and particular. Use initial condition if given.
a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
##Solve for D only
19. Solve the following recurrence equations using the characteristic equation. (a) T(n) = 2T(5/+10g3 n T (1) =0 for n > 1, n a power of 3 (b) T(n) = 10T()+12 T (1) =0 for n > 1, n a power of 5 or nI, na power of 5 (c) nT (n) (n 1)T(n-1)+3 for n> 1 T(1) = 1 (d) nT(n) = 3 (n-1)T(n-1) _ 2 (n-2) T (n-2) +4" T (0) 0 T (1)...
Use generating functions to solve an = 5an-1 + 3, ao = 2.
6. Solve the following recurrence relations: (a) An+1 ,00 = 2 (b) n-1 an+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0