Squared triangular number

A squared triangular number is the square of a triangular number. Its sequence begins 1, 9, 36, 100, and 225.

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Triangular number: A number of the form n(n+1)/2, equal to the number of dots in a triangular arrangement with n rows. Each squared triangular number is formed by squaring one of these numbers.
Pell equation: An equation of the form x² − Dy² = 1, where D is a fixed positive nonsquare integer. The equation x² − 8y² = 1 encodes the triangular-square condition.
1: The positive integer immediately following zero. It is the first squared triangular number, from the triangular number 1.
Square triangular number: A number that is both a perfect square and a triangular number. It names the same values by their shared properties rather than by the act of squaring.
Perfect square: An integer equal to the square of another integer. Every term is a perfect square, with a triangular number as its square root.
Pell sequence: A sequence generated from powers of a fundamental solution to a Pell equation. Its recurrence produces the triangular indices and square roots for successive terms.
9: The positive integer equal to three squared. It is the square of the triangular number 3.
Square number: An integer that is the square of an integer. Unlike arbitrary square numbers, these have triangular square roots.
Figurate number: A number represented by dots arranged in a regular geometric pattern. Squared triangular numbers combine two figurate-number properties: triangularity and squareness.
Linear recurrence: A sequence rule expressing each term as a fixed linear combination of earlier terms. Squared triangular numbers satisfy a recurrence derived from the Pell equation.