The Triangular square number reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Triangular square number

A triangular square number is a number which is both a triangular number and a perfect square. There is an infinity of triangular squares, given by the formula

The k^th triangular square N_k is equal to the s^th perfect square and the t^th triangular number, such that

,

t is given by the formula

.

As k becomes larger, the ratio t/s approaches the square root of two:

External references

• Triangular numbers that are also square. From Interactive Mathematics Miscellany and Puzzles.

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