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

0,5

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.

Links

Table of n, a(n) for n=0..80.

Formula

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

Example

.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.

Sequence in context: A360326 A322976 A011793 * A228106 A334506 A098199

Adjacent sequences: A109646 A109647 A109648 * A109650 A109651 A109652

Keyword

nonn,tabf,easy,changed

Author

Philippe Deléham, Aug 03 2005

Status

approved