A109649 Entries in 3-dimensional version of Pascal triangle: trinomial coefficients.

1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 3, 1, 3, 6, 3, 3, 3, 1, 1, 4, 6, 4, 1, 4, 12, 12, 4, 6, 12, 6, 4, 4, 1, 1, 5, 10, 10, 5, 1, 5, 20, 30, 20, 5, 10, 30, 30, 10, 10, 20, 10, 5, 5, 1, 1, 6, 15, 20, 15, 6, 1, 6, 30, 60, 60, 30, 6, 15, 60, 90, 60, 15, 20, 60, 60, 20, 15, 30, 15, 6

Offset: 0

Author

Philippe Deléham, Aug 03 2005

Keywords

• nonn
• tabf
• easy

Comments

Greatest numbers in each 2D triangle form A022916 (multinomial coefficient n!/([n/3]![(n+1)/3]![(n+2)/3]!)).

2D triangle sums are powers of 3.

See A046816 for another version.

Examples

			.1 3 3 1 ... Here is the third slice of the pyramid
. 3 6 3
.. 3 3
... 1 .....
		

Crossrefs

Cf. A022916, A046816.

Cf. A007318, A002378, A027480, A033487, A033488.

Formula

Coefficients of x, y, z in (x+y+z)^n.