

A092542


Table below read by antidiagonals alternately upwards and downwards.


6



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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

1 1 1 1 1 ...
2 2 2 2 2 ...
3 3 3 3 3 ...
4 4 4 4 4 ...
...
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


REFERENCES

Amir D. Aczel, "The Mystery of the Aleph, Mathematics, the Kabbalah and the Search for Infinity", Barnes & Noble, NY 2000, page 112.


LINKS

Table of n, a(n) for n=1..100.
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.
Eric Weisstein's MathWorld, Pairing functions


FORMULA

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


MATHEMATICA

Table[ Join[Range[2n  1], Reverse@ Range[2n  2]], {n, 8}] // Flatten (* Robert G. Wilson v, Sep 28 2006 *)


CROSSREFS

Cf. A092543, A056011, A056023.
Sequence in context: A159455 A105734 A076839 * A321305 A026552 A333271
Adjacent sequences: A092539 A092540 A092541 * A092543 A092544 A092545


KEYWORD

easy,nonn,tabl


AUTHOR

Sam Alexander, Feb 27 2004


STATUS

approved



