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A213195
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Second inverse function (of columns) for pairing function A211377.
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1
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1, 3, 2, 1, 2, 1, 5, 4, 3, 4, 3, 2, 1, 2, 1, 7, 6, 5, 6, 5, 4, 3, 4, 3, 2, 1, 2, 1, 9, 8, 7, 8, 7, 6, 5, 6, 5, 4, 3, 4, 3, 2, 1, 2, 1, 11, 10, 9, 10, 9, 8, 7, 8, 7, 6, 5, 6, 5, 4, 3, 4, 3, 2, 1, 2, 1, 13, 12, 11, 12, 11, 10, 9, 10, 9, 8, 7, 8, 7, 6, 5, 6, 5, 4, 3, 4, 3, 2, 1, 2, 1
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OFFSET
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1,2
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LINKS
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FORMULA
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See Python program.
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EXAMPLE
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The start of the sequence as triangle array read by rows:
1;
3,2;
1,2,1;
5,4,3,4;
3,2,1,2,1;
7,6,5,6,5,4;
3,4,3,2,1,2,1;
. . .
The start of the sequence as array read by rows, the length of row r is 4*r-3.
First 2*r-2 numbers are from the row number 2*r-2 of above triangle array.
Last 2*r-1 numbers are from the row number 2*r-1 of above triangle array.
1;
3,2,1,2,1;
5,4,3,4,3,2,1,2,1;
7,6,5,6,5,4,3,4,3,2,1,2,1;
...
Row number r is 2*r-1, 2*r-2, 2*r-3, 2*r-2, {row number r-1}.
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PROG
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(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
i=n-t*(t+1)/2
j=(t*t+3*t+4)/2-n
result=((1+(-1)**i)*((1+(-1)**j)*2*int((j+2)/4)-(-1+(-1)**j)*(2*int((i+4)/4)+2*int(j/2)))-(-1+(-1)**i)*((1+(-1)**j)*(1+2*int(i/4)+2*int(j/2))-(-1+(-1)**j)*(1+2*int(j/4))))/4
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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