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## Catalan Numbers with Applications

*Thomas Koshy*

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ... More

## The Central Binomial Coefficient Revisited

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0003
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter continues to investigate the central binomial coefficient in much greater detail. Topics explained include Wallis' product, Lucas numbers, Fermat's little theorem, Carlitz's formula, ... More

## Look for beauty, because of Fibonacci numbers

*Susan D'Agostino*

### in How to Free Your Inner Mathematician: Notes on Mathematics and Life

- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198843597
- eISBN:
- 9780191879388
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198843597.003.0014
- Subject:
- Mathematics, Educational Mathematics, Applied Mathematics

“Look for beauty, because of Fibonacci numbers” explains how to use addition to construct an ordered list of numbers known as the Fibonacci numbers. The chapter explores several unexpected and lovely ... More

## The arithmetical triangle

*A. W. F. EDWARDS*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0008
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The arithmetical triangle is the most famous of all number patterns. Apparently a simple listing of the binomial coefficients, it contains the triangular and pyramidal numbers of ancient Greece, the ... More

## Puzzles

*Anany Levitin and Maria Levitin*

### in Algoristhmic Puzzles

- Published in print:
- 2011
- Published Online:
- November 2020
- ISBN:
- 9780199740444
- eISBN:
- 9780197563021
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199740444.003.0007
- Subject:
- Computer Science, Software Engineering

1. A Wolf, a Goat, and a Cabbage A man finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, ... More

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