cp's OEIS Frontend

A092542 Table whose n-th row is constant and equal to n, read by antidiagonals alternately upwards and downwards.

%I A092542 #40 Feb 16 2025 08:32:52
%S A092542 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 A092542 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 A092542 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 A092542 Table whose n-th row is constant and equal to n, read by antidiagonals alternately upwards and downwards.
%C A092542 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 A092542 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 A092542 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 A092542 Amir D. Aczel, "The Mystery of the Aleph, Mathematics, the Kabbalah and the Search for Infinity", Barnes & Noble, NY 2000, page 112.
%H A092542 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%H A092542 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing functions</a>
%F A092542 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
%e A092542 The table
%e A092542   1 1 1 1 1 ...
%e A092542   2 2 2 2 2 ...
%e A092542   3 3 3 3 3 ...
%e A092542   4 4 4 4 4 ...
%e A092542 gives
%e A092542   1;
%e A092542   1 2;
%e A092542   3 2 1;
%e A092542   1 2 3 4;
%e A092542   5 4 3 2 1;
%e A092542   1 2 3 4 5 6;
%t A092542 Table[ Join[Range[2n - 1], Reverse@ Range[2n - 2]], {n, 8}] // Flatten (* _Robert G. Wilson v_, Sep 28 2006 *)
%Y A092542 Cf. A092543, A056011, A056023.
%Y A092542 Variants of Cantor's enumeration are: A352911, A366191, A319571, A354266.
%K A092542 easy,nonn,tabl
%O A092542 1,3
%A A092542 _Sam Alexander_, Feb 27 2004
%E A092542 Name edited by _Michel Marcus_, Dec 14 2023