Square triangular number: Difference between revisions

Revision as of 20:00, 11 August 2007

Revision as of 02:48, 24 August 2007

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:''For squares of triangular numbers, see [[squared triangular number]]''

A '''square triangular number''' (or '''triangular square number''') is a number which is both a [[triangular number]] and a [[square number|perfect square]]. There isare an [[Infinity|infinite]] number of triangular squares, given by the formula

:<math> N_k = {1 \over 32} \left( \left( 1 + \sqrt{2} \right)^{2k} - \left( 1 - \sqrt{2} \right)^{2k} \right)^2 . </math>

or by the linear [[recursion]]