a) Find a recurrence relation that would determine the number of sequences a1, a2, ., an that have an odd number of zeros when each a, E { 0, 1, 2}, in terms of the number of sequences of n-1 of these elements that do. For example when n=3 we would have the sequences 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222. These sequences consist of all of the base 3 numbers that can be made using 3 digits. = 12 If we let T(n) = # of these sequences with an odd number of 0's, we would get for n=3 that T(3) b) Determine the base condition for this recurrence relation and determine by iteration a closed form formula for the value of the recurrence relation for any number of digits n. C) Prove that your formula is correct.

a) Find a recurrence relation that would determine the number of sequences a1, a2, ., an that have an odd number of zeros when each a, E { 0, 1, 2}, in terms of the number of sequences of n-1 of these elements that do. For example when n=3 we would have the sequences 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222. These sequences consist of all of the base 3 numbers that can be made using 3 digits. = 12 If we let T(n) = # of these sequences with an odd number of 0's, we would get for n=3 that T(3) b) Determine the base condition for this recurrence relation and determine by iteration a closed form formula for the value of the recurrence relation for any number of digits n. C) Prove that your formula is correct.

Name: Discrete mathematics a) Find a recurrence relation that would determin
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Description: Discrete mathematics a) Find a recurrence relation that would determine the number of sequences a1, a2, , anthat have an odd number of zeros when each a, E { 0, 1, 2 }, in terms of the number of sequences ofn-1 of these elements that do.For example w

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Discrete mathematics

a) Find a recurrence relation that would determine the number of sequences a1, a2, , an
that have an odd number of zeros when each a, E { 0, 1, 2 }, in terms of the number of sequences of
n-1 of these elements that do.
For example when n= 3 we would have the sequences 000, 001, 002, 010, 011, 012, 020, 021, 022,
100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222.
These sequences consist of all of the base 3 numbers that can be made using 3 digits.
If we let T(n) = # of these sequences with an odd number of O's, we would get for n=3 that T(3) = 12
%3D
b) Determine the base condition for this recurrence relation and determine by iteration a closed form formula
for the value of the recurrence relation for any number of digits n.
c) Prove that your formula is correct.
OLT+EN+F10 (Mac)

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