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A210535
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Second inverse function (numbers of columns) for pairing function A209293.
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2
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1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 6, 5, 3, 1, 2, 4, 6, 7, 5, 3, 1, 2, 4, 6, 8, 7, 5, 3, 1, 2, 4, 6, 8, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12
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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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a(n) = 2*i-v*(4*i-2*t-3), where t = floor((-1+sqrt(8*n-7))/2), i = n-t*(t+1)/2, v = floor((2*n+1-t*(t+1))/(t+3)).
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EXAMPLE
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The start of the sequence as triangle array read by rows:
1;
2,1;
2,3,1;
2,4,3,1;
2,4,5,3,1;
2,4,6,5,3,1;
2,4,6,7,5,3,1;
2,4,6,8,7,5,3,1;
. . .
Row number r contains permutation numbers from 1 to r: 2,4,6,...2*floor(r/2),2*floor(r/2)-1,2*floor(r/2)-3,...3,1.
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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
v=int((2*n+1-t*(t+1))/(t+3))
result=2*i-v*(4*i-2*t-3)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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