A triomino (not to be confused with a tromino) is an equilateral triangle-shaped tile with numbers in each corner. Like the game of dominoes, the object is to place them next to each other so their numbers match.

The standard set I own with numbers 0 to 5 has 56 tiles. Does the company care about orientation?

Find two formulas for the number of triominoes in a set numbered from 0 to n both considering and not considering orientation.