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A109649 Entries in 3-dimensional version of Pascal triangle: trinomial coefficients. 7
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 (list; graph; refs; listen; history; text; internal format)
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. A007318, A046816, A002378, A027480, A033487, A033488.

Sequence in context: A035176 A322976 A011793 * A228106 A098199 A309474

Adjacent sequences:  A109646 A109647 A109648 * A109650 A109651 A109652

KEYWORD

nonn,tabf,easy

AUTHOR

Philippe Deléham, Aug 03 2005

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)