Seidel-Entringer-Arnold Triangle

Author

Eric W. Weisstein
December 9, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/Seidel-Entringer-ArnoldTriangle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Seidel-Entringer-ArnoldTriangle.html.

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

Enumeration

e[0,0]:=1
e[n_,0]:=0
e[n_,k_]:=e[n,k]=e[n,k-1]+e[n-1,n-k]

ColumnForm[Table[e[n,k],{n,0,5},{k,0,n}],Center]

Flatten[Sequence@@{Reverse[#[[1]]],#[[2]]}&/@Partition[Table[e[n,k],{n,0,5},{k,0,n}],2]]

ColumnForm[Sequence@@{Reverse[#[[1]]],#[[2]]}&/@Partition[Table[e[n,k],{n,0,5},{k,0,n}],2],Center]

Binary Plot

<<Utilities`Plot`

Length[t=Flatten[Sequence@@{Reverse[#[[1]]],#[[2]]}&/@Partition[Table[e[n,k],{n,0,35},{k,0,n}],2]]]

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

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