

A125512


Array x read by diagonals, where x(i,j) = floor((T(i,j1)+T(i,j+1))/2) for i>=0 and j>=0. Here T is Wythoff's array A035513.


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1, 2, 5, 3, 7, 7, 5, 12, 11, 10, 9, 20, 18, 16, 14, 14, 32, 29, 27, 22, 16, 23, 52, 47, 43, 36, 25, 19, 38, 85, 76, 70, 58, 41, 31, 21, 61, 137, 123, 114, 94, 67, 50, 34, 25, 99, 222, 199, 184, 152, 108, 81, 56, 40, 28, 161, 360, 322, 298, 246, 175, 132, 90, 65, 45
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OFFSET

0,2


COMMENTS

x(i,j)*(x(i,j) + (T(i,j) mod 2)) = (5*T(i,j)^2  (T(i,j) mod 2))/4 + A(i)*(1)^j, where A(i)=A022344(i).


LINKS



FORMULA

For j>1, x(i,j) = x(i,j1) + x(i,j2) + (T(i,j1)*T(i,j2) mod 2).


EXAMPLE

x(2,4)=floor((T(2,3)+T(2,5))/2)=floor((26+68)/2)=47. Since T(2,4)=42 and A(2)=4, the equation in the first comment becomes 47*(47+0) = (5*42^20)/4 + 4*(1)^4.


MATHEMATICA

T[i_, j_]:=i*Fibonacci[j+1]+Fibonacci[j+2]*Floor[(i+1)(1+Sqrt[5])/2]; x[i_, j_]:=Floor[(T[i, j1]+T[i, j+1])/2]


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EXTENSIONS



STATUS

approved



