Question

1. ) Find a closed form for the generating function for each of the following sequences:

1. an=5-2n

2. 0, 0, 0, 4, -12, 36, -108

3. 0, 1, 0, 4, 0, 16, 0, 64, 0, …

Answer 1

An= 5-an. let fa= Ž an an be generating function for no the given sequence fm (5- 2n) en nzo an 11. 52n 2. nel: nzo = 5. S an 22 næn-l nao nal 5.11-2 2a: ( > den a) 12 nanya co 2% nal 1) 5192) (1 m) 17 5- FX -2)*

2 0, 0, 0, 4,-12, 36, -108 The comes esponding genenating function is fat QJ = 0 - + - 2 4. 0.8e2f43e 3-12x44 3635-108 at 423 1229+ 8685-10826 483 (1- 3x +9**_2723) - 42% (1-63 834) it 3a 11 433 (1-8784) 14 3x 3 0, 1, 0, 4,0, 16, 0, 64,0., Let the comes spanding genenating function be gla) gla)= x-tuzº+ 1625 +642.7 # sa(1+ If 4x²+ 16 se lip 64 x 6 + . X. l-ian 17. |-422