1994 AIME Problem 11

Ninety-four bricks, each measuring 4''\times10''\times19'', are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes 4''\, or 10''\, or 19''\, to the total height of the tower. How many different tower heights can be achieved using all 94 of the bricks?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.