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Exploring Pascal || Student Center || Teachers' Place
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Hexagonal numbers are figurate numbers (numbers that can be represented by a regular geometric arrangement of equally spaced points), and 6-polygonal numbers of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... . Every hexagonal number is also a triangular number.

Like the triangular numbers, the hexagonal numbers are found in the third diagonal of Pascal's triangle:

 
 

 

 

 

 

 

 

 

 1

 

 

 

 

 

 

 

 

   Row 0
 

 

 

 

 

 

 

 1

 

 1

 

 

 

 

 

 

 

   Row 1
 

 

 

 

 

 

 1

 

 2

 

 1

 

 

 

 

 

 

   Row 2
 

 

 

 

 

  1

 

 3

 

 3

 

 1

 

 

 

 

 

   Row 3
 

 

 

 

 1

 

 4

 

 6

 

 4

 

 1

 

 

 

 

   Row 4
 

 

 

 1

 

 5

 

10

 

10

 

 5

 

 1

 

 

 

   Row 5
 

 

 1

 

 6

 

15

 

20

 

15

 

 6

 

 1

 

 

   Row 6
 

 1

 

 7

 

21

 

35

 

35

 

21

 

 7

 

 1

 

   Row 7
 1

 

 8

 

28

 

56

 

70

 

56

 

28

 

 8

 

 1

   Row 8

References

  1. Eric's Treasure Trove of Mathematics: Figurate Number, Hexagonal Number


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