7. Let r, be the number of different reversible trains of length nwhich are built out of cars which are either 1 unit long or 2 unitslong. This is the same as the standard train problem, except the5-trains 122 and 221 are no longer considered different, becauseThe 5 reversible trains oflength 51-1-1-1-1one is the same as the other in reverse order. But the train 212 is1-1-1-21-1-2-1different from these. For example, rs = 5 (table at the right).Find a formula for r, in terms of the Fibonacci numbers. Can1-2-22-1-2you find a general argument for your formula?

7. Let r, be the number of different reversible trains of length n which are built out of cars which are either 1 unit long or 2 units long. This is the same as the standard train problem, except the 5-trains 122 and 221 are no longer considered different, because one is the same as the other in reverse order. But the train 212 is different from these. For example, rs = 5 (table at the right). Find a formula for r, in terms of the Fibonacci numbers. Can %3D you find a general argument for your formula?

7. Let r, be the number of different reversible trains of length n which are built out of cars which are either 1 unit long or 2 units long. This is the same as the standard train problem, except the 5-trains 122 and 221 are no longer considered different, because one is the same as the other in reverse order. But the train 212 is different from these. For example, rs = 5 (table at the right). Find a formula for r, in terms of the Fibonacci numbers. Can %3D you find a general argument for your formula?

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

7. Let r, be the number of different reversible trains of length n
which are built out of cars which are either 1 unit long or 2 units
long. This is the same as the standard train problem, except the
5-trains 122 and 221 are no longer considered different, because
The 5 reversible trains of
length 5
1-1-1-1-1
one is the same as the other in reverse order. But the train 212 is
1-1-1-2
1-1-2-1
different from these. For example, rs = 5 (table at the right).
Find a formula for r, in terms of the Fibonacci numbers. Can
1-2-2
2-1-2
you find a general argument for your formula?

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