Question

Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms.

(a) (1−x)G−4/x

(b) (1−x)G−4/x^3

(c) (1−x)G+6/x

(d) (1−x)G−x^2

This question was addressed to me in a job interview.

Origin of the question is Discrete Probability topic in section Discrete Probability of Discrete Mathematics

Answer 1

The correct answer is (a) (1−x)G−4/x

The explanation: (1−x)G = 4 + 3x + 6x^2 + 9x^3 +⋯ which can be accepted. We can compute it like this:

3 + 6x + 9x^2 + ⋯ = (1−x)G−4/x.