MATH 145: HOMEWORK 4
ANDREW BERGET
This is due
Friday February 5!
Problem A.
When I write “Determine the generating function”, I mean write the generating function
in a closed, simple form.
(1) [Determine the generating function of the constant sequence
a
n
= 1.]
(2) [Determine the generating function of the nearly constant sequence
a
n
= 5 if
n
≥
3000 and
a
n
= 0
if 0
≤
n <
3000.]
(3) [Determine the generating function of the sequence
a
n
which is 0 unless 3
≤
n
≤
20, in which case
a
n
= 4.]
(4) (2 points) Determine the generating function for the sequence
a
n
, which is number of subsets of a
set of size
n
.
(5) (2 points) Determine the generating function for the number
a
k
of subsets of [
n
] with
k
elements.
(6) (2 points) Determine the generating function for the sequence
a
n
determined by the condition that
a
n
is zero if
n
is odd and is 3
n
if
n
is even.
(7) (2 points)Determine the generating function for the sequence
a
n
determined by the condition that
a
n
is zero if
n
is even and is 2
n
if
n
is odd.
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 Winter '07
 Peche
 Math, Combinatorics, Natural number, 0 1 2 m, ANDREW BERGET

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