# Homework Nine - Quick Answers

1. C(12,6)

2. Generator is (1+x+x2)50 seek coefficient of x40 This begins C(89,40)-C(50,1)*C(86,37)+C(50,2)*C(83,34)...

3. Just pick the first 15 - the first pile. Then the second pile is forced. The generator: (1+x+x2+....+x5)6 seek coefficient of x15 in this expression

4. Use these exponential generators: (ex - x2/2)3 and ex((ex + e-x)/2)2.

a) 3**r - 3*C(r,2)*2**(r-2) + 3C(r,2)*C(r-2,2); b) 1/4(3**r - 4*2**r +6 + (-1)**r)

5. an = an-3 + an-5 + an-10

6. an = an-1 + an-2 ; an = 2an-1 + 2an-2 ; an = an-1 + 2an-2 + 2an-3 + 2an-4 + ....

7. Write down sn = sn-1 + sn-2, examine termwise, and use the relationship C(N,k) = C(N-1,k) + C(N-1,k-1) to pair up terms on the right hand side

8. an = 2an-1; solution is an = 3*2n.

-- RobbieMoll - 2012-05-03

Topic revision: r6 - 2014-12-08 - RobbieMoll

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