Tell whether or not each of the following recurrence relation given below is a l

Question

Tell whether or not each of the following recurrence relation given below is a linear homogeneous recurrence relation with constant coefficients. For those that are linear homogenous recurrence relation with constant coefficients, give their order. Find a recurrence relation, with initial condition, that uniquely determines the sequences: 9, 2, -5, -12,... 3, 5, 8, 13, 21.... 2, 7, 17, 37, 77... Obtain an explicit formula for the recurrence relation you found in (i) in part (a) above. Verify your result. Find an explicit formula for each of the following recurrence relations. a_n = a_n - 1 - 3, n 1 a_0 = 5 Determine whether or not each of the following sequence of nonnegative integers represent degree sequence of a graph. 3, 3, 3, 3, 3, -2, 2, 1

Explanation / Answer

2.

Recurrence relation

Linear?

Homogenous?

With constant coefficients

Degree

yes

yes

yes

3

yes

No

yes

Constant function ()should not present

yes

no

no

Coefficients must be constant .

Should not

No

yes

yes

3.

a)

(i) 9,2,-5,-12,…

Thus the recurrence relation

With Initial conditions

(ii)

3,5,8,13,21,…

Thus the recurrence relation

With Initial conditions
(iii)

2,7,17,37,77…

Thus the recurrence relation

With Initial conditions

Recurrence relation

Linear?

Homogenous?

With constant coefficients

Degree

yes

yes

yes

3

yes

No

yes

Constant function ()should not present

yes

no

no

Coefficients must be constant .

Should not

No

yes

yes

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