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Search: id:A046816
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| A046816 |
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Entries in 3-dimensional version of Pascal triangle: trinomial coefficients. |
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+0
13
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| 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 3, 3, 3, 6, 3, 1, 3, 3, 1, 1, 4, 4, 6, 12, 6, 4, 12, 12, 4, 1, 4, 6, 4, 1, 1, 5, 5, 10, 20, 10, 10, 30, 30, 10, 5, 20, 30, 20, 5, 1, 5, 10, 10, 5, 1, 1, 6, 6, 15, 30, 15, 20, 60, 60, 20, 15, 60, 90, 60, 15, 6, 30, 60, 60, 30, 6, 1, 6, 15, 20, 15, 6, 1
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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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. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Aug 15 2004
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FORMULA
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Coefficients of x, y, z in (x+y+z)^n: a(i+1, k, j) = a(i, k, j)+a(i, j, k-1)+a(i, j-1, k-1), a(i, j, -1) := 0, ...; a(0, 0, 0)=1.
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EXAMPLE
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... 1 .... Here is the third slice of the pyramid
.. 3 3
. 3 6 3
.1 3 3 1
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CROSSREFS
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Cf. A007318.
Entry [3,2] in each slice gives A002378, entry [4,3] in each slice gives A027480, entry [5,2] in each slice gives A033488, entry [5,3] in each slice gives A033487.
Sequence in context: A097456 A087775 A089955 this_sequence A138328 A137264 A078614
Adjacent sequences: A046813 A046814 A046815 this_sequence A046817 A046818 A046819
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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Lior Manor (lior.manor(AT)gmail.com)
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