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A109649
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Entries in 3-dimensional version of Pascal triangle: trinomial coefficients.
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7
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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; internal format)
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OFFSET
| 0,5
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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.
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FORMULA
| Coefficients of x, y, z in (x+y+z)^n.
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EXAMPLE
| .1 3 3 1 ... Here is the third slice of the pyramid
. 3 6 3
.. 3 3
... 1 .....
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CROSSREFS
| Cf. A007318, A046816, A002378, A027480, A033487, A033488.
Sequence in context: A143786 A035176 A011793 * A098199 A022828 A129406
Adjacent sequences: A109646 A109647 A109648 * A109650 A109651 A109652
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KEYWORD
| nonn,tabf,easy
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 03 2005
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