A Number Pyramid is composed of the 10 different numbers 0-9 with a top row of 1 number resting on a second row of 2 sitting on a third row of 3 supported by a bottom row of 4. For example, a Number Pyramid could be:

0
1 2
3 4 5
6 7 8 9

(Note: Its a pyramid shape.I was not able to represent it fully)


Given the clues below, can you determine the composition of Number Pyramid ?
The three numbers at the top of Number Pyramid sum to 17, with the largest of the three atop the pyramid.
The 2 isn't in the pyramid's third row, where the three numbers sum to 8.
The leftmost number in the bottom row minus the number to its immediate right equals 1.
The four leftmost numbers in the four rows of the pyramid add up to 13.
The rightmost numbers in the two bottom rows sum to 11.