Square triangular number: Difference between revisions

Revision as of 17:28, 21 July 2007

Revision as of 20:00, 11 August 2007

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or by the linear [[recursion]]

:<math>N_k = 34N_{k-1} - N_{k-2} + 2</math> with <math>N_0 = 0</math> and <math>N_1 = 1</math>

The first few square triangular numbers are [[1 (number)|1]], [[36 (number)|36]], 1225, 41616, 1413721, 48024900, 1631432881, 55420693056, 1882672131025, ... {{OEIS|id=A001110}}

The problem of finding square triangular numbers reduces to [[Pell's equation]] in the following way. Every triangular number is of the form ''n''(''n'' + 1)/2. Therefore we seek integers ''n'', ''m'' such that