Floyd's triangle

Floyd's triangle is a right-angled triangular array of natural numbers, used in computer science education. It is named after Robert Floyd. It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner:

1
2	3
4	5	6
7	8	9	10
11	12	13	14	15

Beginning programmers are often assigned the task of writing a program to print out the table in the format shown.^[1]^[2]

Properties

The numbers along the left edge of the triangle are the lazy caterer's sequence and the numbers along the right edge are the triangular numbers. The nth row sums to $n (n 2 + 1)/2$ , the constant of an $n \times n$ magic square (sequence A006003 in the OEIS).

Summing up the row sums in Floyd's triangle reveals the doubly triangular numbers (triangular numbers with an index that is triangular)(sequence A002817 in the OEIS)^[3]

1            = 1 = T(T(1))

1            = 6 = T(T(2))
2 + 3

1
2 + 3     = 21 = T(T(3))
4 + 5 + 6

Each number in the triangle is smaller then number below it by the index of its row.

References

^ Keller, Arthur M. (1982), A first course in computer programming using PASCAL, McGraw-Hill, p. 39.
^ Peters, James F. (1986), Pascal with program design, Holt, Rinehart and Winston, pp. 137, 154.
^ Foster, Tony (2015), Doubly Triangular Numbers OEIS A002817.

External links

Floyd's triangle at Rosetta code

[1] Keller, Arthur M. (1982), A first course in computer programming using PASCAL, McGraw-Hill, p. 39.

[2] Peters, James F. (1986), Pascal with program design, Holt, Rinehart and Winston, pp. 137, 154.

[3] Foster, Tony (2015), Doubly Triangular Numbers OEIS A002817.

[1]

[2]

[3]

Properties

See also

References

External links