Trinomial Triangle

Author

Eric W. Weisstein
December 9, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/TrinomialTriangle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TrinomialTriangle.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

ColumnForm[Table[CoefficientList[(1+x+x^2)^n,x],{n,0,6}],Center]

Normal[Series[(1/(1-z(1+w+w^2))),{w,0,5},{z,0,5}]]//TraditionalForm

CoefficientList[Normal[Series[(1/(1-z(1+w+w^2))),{z,0,5},{w,0,5}]],{z,w}]

Binary Plot

<<Utilities`Plot`

Length[t=Flatten[Table[CoefficientList[(1+x+x^2)^n,x],{n,0,25}]]]

Show[PixelPerfect[BasePlot[Take[t,255]],BlockSize->2]]

Show[PixelPerfect[BasePlot[Take[t,511]],BlockSize->1]]