Wythoff's square array is Sloane's reference A035513 in the online encyclopedia of sequences (click the "table" button to see the sequence as a table) and Allan Wechsler's sequence is A022344. To my knowledge the following connection has not been noted before.(adsbygoogle = window.adsbygoogle || []).push({});

Let T(i,j) be defined from the table as follows T(1,1) = 1, T(1,2) = 2 and T(2,1) = 4 and let A(i) be the Wechsler's sequence starting with A(1) = 1

Then x(i,j) are integers defined by the following relation:

If T(i,j) is even then

[tex]\frac{5*T_{(i,j)}^{2}}{4} - A_{i}*(-1)^{i} = x_{(i,j)}^{2} [/tex]

If T(i,j) is odd then

[tex]\frac{5*T_{(i,j)}^{2} - 1}{4} -A_{i}*(-1)^{i} = x_{(i,j)}^{2} + x_{(i,j)}[/tex]

for j>2 and [tex]T_{(i,j)}[/tex] is odd

[tex]x_{(i,j)} = x_{(i,j-1)} + x_{(i,j-2)} [\tex]

for j>2 and [tex]T_{(i,j)}[/tex] is even

[tex]x_{(i,j)} = x_{(i,j-1)} + x_{(i,j-2)} + 1[\tex]

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# Wythoff' array and Wechsler's Sequence

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