# For n ¥ 1, let tn count the number of spanning trees for the fan on n + 1 vertices.

## Question:

(a) Show that tn+1 = tn + ˆ‘nl=0 tl, where n ‰¥ 1 and t0 = 1.

(b) For n ‰¥ 2, show that tn+1 = 3tn - tn-1.

(c) Solve the recurrence relation in part (b) and show that for n ‰¥ 1, tn = F2n, the 2nth Fibonacci number.

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## Step by Step Answer:

**Related Book For**

## Discrete and Combinatorial Mathematics An Applied Introduction

**ISBN:** 978-0201726343

5th edition

**Authors:** Ralph P. Grimaldi

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