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
The sequences Nk, sk and tk are the OEIS sequences A001110, A001109, and A001108 respectively.
In 1778 Leonhard Euler determined the explicit formula
Other equivalent formulas (obtained by expanding this formula) that may be convenient include
The corresponding explicit formulas for sk and tk are
and
Read more about this topic: Square Triangular Number
Famous quotes containing the words explicit and/or formulas:
“I think taste is a social concept and not an artistic one. Im willing to show good taste, if I can, in somebody elses living room, but our reading life is too short for a writer to be in any way polite. Since his words enter into anothers brain in silence and intimacy, he should be as honest and explicit as we are with ourselves.”
—John Updike (b. 1932)
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (18771962)