
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square. There are an infinite number of square triangular numbers; the first few are 0, 1, 36, 1225, 41616, 1413721, 48024900, 1631432881, 55420693056, 1882672131025 (sequence A001110 in OEIS).
== Explicit formulas ==
Write Nk for the kth square triangular number, and write sk and tk for the sides of the corresponding square and triangle, so that
Define the triangular root of a triangular number to be . From this definition and the quadratic formula, Therefore...