1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to find a difference polynomial?

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Let {a_n} be the sequence 3, 4, 8, 17,..., where a_0 = 3 and a_n+1 = a_n + (n+1)^2, n greater than or equal to 0. Find a polynomial such that a_n = f(n)

    2. Relevant equations

    f(n) = summation from r=0 to infinity of C(n,r) delta^r a_0

    3. The attempt at a solution

    I just have no idea how to start it. I have: f(n) = 3C(n, 0) + 4C(n, 1) + 8C(n,2) + something?
  2. jcsd
  3. Nov 26, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Look at the differences

    1,4,9,... is just the sequence for n2

    So f(n+1)-f(n) = n2. If the difference has degree k, the actual polynomial has degree k+1 (something you should try proving) so find a cubic polynomial with this characteristic
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?