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A092543 Table below read by antidiagonals alternately upwards and downwards. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

Eric Weisstein's MathWorld, Pairing functions

FORMULA

T(r,c)=c.

A092542(n)+a(n) = 1+A002024(n). - Enrique Pérez Herrero, Apr 01 2010

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

MAPLE

seq(seq(i-abs(i-j), j=1..2*i-1), i=2..20, 2); # Robert Israel, Mar 01 2016

MATHEMATICA

Table[ Join[Range[2n], Reverse@Range[2n - 1]], {n, 7}] // Flatten (* Robert G. Wilson v, Sep 28 2006 *)

CROSSREFS

Cf. A092542, A056011, A056023.

Sequence in context: A289816 A054482 A208234 * A277083 A216222 A090282

Adjacent sequences:  A092540 A092541 A092542 * A092544 A092545 A092546

KEYWORD

nonn,easy,tabl

AUTHOR

Sam Alexander, Feb 27 2004

STATUS

approved

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Last modified September 25 00:02 EDT 2020. Contains 337333 sequences. (Running on oeis4.)