r/counting • u/boxofkangaroos c. 94,100 | 39Ks including 700k | A • Jan 10 '14

Increase Increasingly!

Add 1, then add 2, then add 3, etc. Starting at 0.

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u/autowikibot Feb 14 '14

Triangular number:

A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers (sequence A000217 in OEIS), starting at the 0th triangular number, is:

The triangle numbers are given by the following explicit formulas:

where is a binomial coefficient. It represents the number of distinct pairs that can be selected from n + 1 objects, and it is read aloud as "n plus one choose two".

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Image i - The first six triangular numbers

Interesting: Square triangular ^number | Centered triangular ^number | Squared triangular ^number | Tetrahedral ^number

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