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Trinomial Triangle


The trinomial triangle is a number triangle of trinomial coefficients. It can be obtained by starting with a row containing a single "1" and the next row containing three 1s and then letting subsequent row elements be computed by summing the elements above to the left, directly above, and above to the right:

 1
1   1   1
1   2   3   2   1
1   3   6   7   6   3   1
1  4  10  16  19  16  10  4  1

(OEIS A027907).

Binary plot for the trinomial triangle

The plot above shows the binary representations for the first 255 (top figure) and 511 (bottom figure) terms of a flattened trinomial triangle.


See also

Central Trinomial Coefficient, Pascal's Triangle, Trinomial, Trinomial Coefficient

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References

Sloane, N. J. A. Sequence A027907 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Trinomial Triangle

Cite this as:

Weisstein, Eric W. "Trinomial Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrinomialTriangle.html

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