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[[File:square_triangular_number_36.svg|234px|thumb|Square triangular number 36 depicted as a triangular number and as a square number.]]
In [[mathematics]], a '''square triangular number''' (or '''triangular square number''') is a number which is both a [[triangular number]] and a [[square number]], in other words, the sum of all integers from <math>1</math> to <math>n</math> has a square root that is an integer. There are [[Infinity|infinitely many]] square triangular numbers; the first few are:
{{bi|left=1.6|0, 1, 36, {{val|1225}}, {{val|41616}}, {{val|1413721}}, {{val|48024900}}, {{val|1631432881}}, {{val|55420693056}}, {{val|1882672131025}} {{OEIS|id=A001110}}}}
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{{bi|left=1.6|<math>\displaystyle s_k = y_k , \quad t_k = \frac{x_k - 1}{2}, \quad N_k = y_k^2.</math>}}
Hence, the first square triangular number, derived from <math>(3,1)</math>, is <math>1</math>, and the next, derived from <math>6\cdot (3,1)-(1,0)
The sequences <math>N_k</math>, <math>s_k</math> and <math>t_k</math> are the [[OEIS]] sequences {{OEIS2C|id=A001110}}, {{OEIS2C|id=A001109}}, and {{OEIS2C|id=A001108}} respectively.
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