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(i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an: the number of distinct ways the pixie can climb a flight of n steps. Also find a1, a2, a3, and a4. (ii) Find a closed form for the generating function for this recurrence relation [please do not find the coefficients of the generating function].

(i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an: the number of distinct ways the pixie can climb a flight of n steps. Also find a1, a2, a3, and a4. (ii) Find a closed form for the generating function for this recurrence relation [please do not find the coefficients of the generating function].

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(b) (i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an: the number of distinct ways the pixie can climb a flight of n steps. Also find a₁, a2, a3, and a4. (ii) Find a closed form for the generating function for this recurrence relation [please do not find the coefficients of the generating function].
Transcribed Image Text:(b) (i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an: the number of distinct ways the pixie can climb a flight of n steps. Also find a₁, a2, a3, and a4. (ii) Find a closed form for the generating function for this recurrence relation [please do not find the coefficients of the generating function].
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