%I
%S 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,
%T 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,
%U 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
%N Table below read by antidiagonals alternately upwards and downwards.
%C 1 1 1 1 1 ...
%C 2 2 2 2 2 ...
%C 3 3 3 3 3 ...
%C 4 4 4 4 4 ...
%C ...
%C 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
%C 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
%C 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
%D Amir D. Aczel, "The Mystery of the Aleph, Mathematics, the Kabbalah and the Search for Infinity", Barnes & Noble, NY 2000, page 112.
%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO], 2012.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing functions</a>
%F a(n) = ((1)^t+1)*j)/2((1)^t1)*i/2, where i=nt*(t+1)/2, j=(t*t+3*t+4)/2n, t=floor((1+sqrt(8*n7))/2).  _Boris Putievskiy_, Dec 24 2012
%t Table[ Join[Range[2n  1], Reverse@ Range[2n  2]], {n, 8}] // Flatten (* _Robert G. Wilson v_, Sep 28 2006 *)
%Y Cf. A092543, A056011, A056023.
%K easy,nonn,tabl
%O 1,3
%A _Sam Alexander_, Feb 27 2004
