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6 Recursion Problems - Applied Combinatorics | MATH 3134, Assignments of Mathematics

Virginia Polytechnic Institute and State University (Virginia Tech)Mathematics
Prof. James E. Shockley

Material Type: Assignment; Professor: Shockley; Class: Applied Combinatorics; Subject: Mathematics; University: Virginia Polytechnic Institute And State University; Term: Spring 2009;

Typology: Assignments

Pre 2010

Uploaded on 05/14/2009

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Math 3134 Recursion Problems
Find a closed formula for an.
1. an + 2an-1 − 3an-2 = 0, a0 = 1, a1 = 5
2. an + 6an-1 + 5an-2 = 0, a0 = 0, a1 = 8
3. an − 4an-1 + 4an-2 = 0, a0 = 2, a1 = 6
4. an − 6an-1 + 11an-2 − 6an-3 = 0, a0 = 8, a1 = 12, a2 = 22
[Hint: r = 1 is a root of the characteristic equation]
5. an + 2an-1 − 3an-2 = 5 ⋅ 2n, a0 = 9, a1 = 5
6. an + 6an-1 + 5an-2 = 36n, a0 = 7, a1 = 0

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Math 3134 Recursion Problems

Find a closed formula for a (^) n.

  1. an + 2an-1 − 3an-2 = 0, a 0 = 1, a 1 = 5
  2. an + 6an-1 + 5an-2 = 0, a 0 = 0, a 1 = 8
  3. an − 4an-1 + 4an-2 = 0, a 0 = 2, a 1 = 6
  4. an − 6an-1 + 11an-2 − 6an-3 = 0, a 0 = 8, a 1 = 12, a 2 = 22 [Hint: r = 1 is a root of the characteristic equation]
  5. an + 2an-1 − 3an-2 = 5 ⋅ 2 n, a 0 = 9, a 1 = 5
  6. an + 6an-1 + 5an-2 = 36n, a 0 = 7, a 1 = 0