6. Find a sequence, An, which has the generating function 1+ 4. 3.2 - 4.0 +1...
Section 1.7: 4. Let f(x) be the exponential generating funcion of a sequence {%). Find the exponential generating functions for the follow- ing sequences in terms of f(x): (a) fan cl (b) foan (c (nani (e) 0, a,a, , (g) ao,0, a2,0, a,0,... (h) a, a2, a,... 8. (a) A sequence a satisfies the recurrence relation a3an+2, ao0 Find the exponential generating function ΣΧ0Lnz"
Section 1.7: 4. Let f(x) be the exponential generating funcion of a sequence {%). Find the...
4) (a) Find the e sequence generated by the generating function by (b) Find the generating function for the sequence 2,0, 4, 0,6,o,8,0,....
5. Find functional equation for the generating function (series) Σαηχη with recurrence relation an-Di-lgian-i-
5. Find functional equation for the generating function (series) Σαηχη with recurrence relation an-Di-lgian-i-
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
( (b) (6 pts.) Find a homogeneous recurrence relation that is satisfied by the following sequence : hn 3(-2)" +4n7
( (b) (6 pts.) Find a homogeneous recurrence relation that is satisfied by the following sequence : hn 3(-2)" +4n7
6. (a) (6 pts.) Find the most general solution to the following recurrence relation: am5am-1-3an-2-9am-3 ( (b) (6 pts.) Find a homogeneous recurrence relation that is satisfied by the following sequence : hn 3(-2)" +4n7
6. (a) (6 pts.) Find the most general solution to the following recurrence relation: am5am-1-3an-2-9am-3
( (b) (6 pts.) Find a homogeneous recurrence relation that is satisfied by the following sequence : hn 3(-2)" +4n7
Consider the sequence {fn}nzo with recurrence given by fo = 1 and п ("+")s.-6 in > 1 i=0 Find its exponential generating function E(2).
2. a) Find the recurrence relation representing the terms of the following sequence: 2, 6, 18, 54. b) Use the Substitution technique (forward or backward) to solve the recurrence relation. Give the e notation of the solution.
Check all that apply. The recurrence relation: hn = hn-1 + 2n – 1 for all n > 1 is recurrence relation. non-linear homogeneous degree 1 linear degree 2 inhomogeneous ? ع (5) م = (2)What equals the generating function A 0 2k=0 (k+5 k (1-2) 4 1 O (1-2) 4 1 (1-2) 6 (1-2) 6 What is the generating function A(z) of the sequence a = (1, 2, 4, 8, ...)? 2 1-22 1 (1-2)? 2 1-2 OO 1...
algebraic combinatoric
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued 4 and
1. Let b be the number of ways to change 6 cents. Find the generating function ". For which n we can actually change n cents this way (that is, bn > 0)? n cents using coins valued...