Unformatted text preview: n that do not have two consecutive 0's. Find a recurrence relation for and use the recurrence relation to findHint – think of how many “good” sequences begin with 1, how many with 2, and how many with 0 (which you will have to break into a few cases). 6) Solve the recurrence relation Hints – First find a particular solution. Then note the roots of the characteristic equation of the associated homogenous relation can be written as . Use that to show that the general solution to the homogeneous equation can be written as. Add the particular solution and match the initial conditions. 7) For the nonlinear equation and use Excel or a short computer program to find to three significant digits. What can you conjecture about for large n ? What changes if you start with...
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 Spring '11
 FredPhelps
 Math, Algebra, Characteristic polynomial, Heterogeneity, Recurrence relation, Homogeneity

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