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A092543
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Table below read by antidiagonals alternately upwards and downwards.
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6
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1, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 12, 11, 10, 9, 8
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OFFSET
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1,2
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COMMENTS
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1 2 3 4 5 ...
1 2 3 4 5 ...
1 2 3 4 5 ...
1 2 3 4 5 ...
...
Let A be sequence A092543 (this sequence) and B be sequence A092542 (1, 1, 2, 3, 2, 1, 1, ...). 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(4) = 1 and B(4) = 3 because the 1 in A(4) is the third 1 to appear in A. - Kerry Mitchell, Dec 28 2005
First inverse function (numbers of rows) for pairing function A056011 and second inverse function (numbers of columns) for pairing function A056023. - Boris Putievskiy, Dec 24 2012
The rational numbers A092542(n)/a(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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T(r,c)=c.
a(n) = ((-1)^t+1)*i/2-((-1)^t-1)*j)/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
G.f.: (1-x)^(-2)*Sum_{i>=0} x^(2*i^2+i+1)*(1-x^(2*i+2))^2. - Robert Israel, Mar 01 2016
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MAPLE
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seq(seq(i-abs(i-j), j=1..2*i-1), i=2..20, 2); # Robert Israel, Mar 01 2016
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MATHEMATICA
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Table[ Join[Range[2n], Reverse@Range[2n - 1]], {n, 7}] // 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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STATUS
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approved
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