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A092542
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Table whose n-th row is constant and equal to n, read by antidiagonals alternately upwards and downwards.
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8
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1, 1, 2, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9
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OFFSET
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1,3
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COMMENTS
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Let A be sequence A092542 (this sequence) and B be sequence A092543 (1, 2, 1, 1, 2, 3, 4, ...). Under upper trimming or lower trimming, A transforms into B and B transforms into A. Also, B gives the number of times each element of A appears. For example, A(7) = 1 and B(7) = 4 because the 1 in A(7) is the fourth 1 to appear in A. - Kerry Mitchell, Dec 28 2005
First inverse function (numbers of rows) for pairing function A056023 and second inverse function (numbers of columns) for pairing function A056011. - Boris Putievskiy, Dec 24 2012
The rational numbers a(n)/A092543(n) can be systematically ordered and numbered in this way, as Georg Cantor first proved in 1873. - Martin Renner, Jun 05 2016
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REFERENCES
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Amir D. Aczel, "The Mystery of the Aleph, Mathematics, the Kabbalah and the Search for Infinity", Barnes & Noble, NY 2000, page 112.
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LINKS
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FORMULA
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a(n) = ((-1)^t+1)*j)/2-((-1)^t-1)*i/2, where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 24 2012
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EXAMPLE
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The table
1 1 1 1 1 ...
2 2 2 2 2 ...
3 3 3 3 3 ...
4 4 4 4 4 ...
gives
1;
1 2;
3 2 1;
1 2 3 4;
5 4 3 2 1;
1 2 3 4 5 6;
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MATHEMATICA
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Table[ Join[Range[2n - 1], Reverse@ Range[2n - 2]], {n, 8}] // Flatten (* Robert G. Wilson v, Sep 28 2006 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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