Wythoff Array

Author

Eric W. Weisstein
June 3, 2003

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

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

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

First Column

Table[Floor[n GoldenRatio]+n-1,{n,20}]

Table[Floor[Floor[n GoldenRatio]GoldenRatio],{n,20}]

Offsets

-Subtract@@@Partition[Table[Floor[Floor[n GoldenRatio]GoldenRatio],{n,100}],2,1]

A001950/M1332

Position[%57,2]//Flatten

Table[Floor[n GoldenRatio^2],{n,10}]

A000201/M2322

Position[%,3]//Flatten

Table[Floor[n GoldenRatio],{n,10}]

Array

WythoffArray[n_]:=Module[
{
i,
nmax,
a=Table[False,{n-1}],
f=Fibonacci[Range[3,n+3]],
f1,f2
},
nmax=i/.FindRoot[Floor[i GoldenRatio]==n,{i,1,2n}];
a[[Floor[Range[nmax-1] GoldenRatio]]]=True;
f1=Drop[f,-1];
f2=Rest[f];
FoldList[Plus,Fibonacci[Range[2,n+1]],If[#,f2,f1]&/@a]
]

TableForm[
Transpose@Table[Fibonacci[k+1]Floor[n GoldenRatio]+Fibonacci[k](n-1),{k,8},{n,8}],TableAlignments->Right]

TableForm[a=WythoffArray[8],TableAlignments->Right]