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A196199 Count up from -n to n for n = 0, 1, 2, ... . 3
0, -1, 0, 1, -2, -1, 0, 1, 2, -3, -2, -1, 0, 1, 2, 3, -4, -3, -2, -1, 0, 1, 2, 3, 4, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

This sequence contains every integer infinitely often, hence all integer sequences are subsequences.

This is a fractal sequence.

REFERENCES

Miklós Laczkovich, Conjecture and Proof, TypoTex, Budapest, 1998. See Chapter 10.

LINKS

Reinhard Zumkeller, Rows n=0..100 of triangle, flattened

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

FORMULA

a(n) = n - t*t - t - 1, where t = floor(sqrt(n-1)). - Boris Putievskiy, Jan 28 2013

EXAMPLE

Table starts:

0,

-1, 0, 1,

-2, -1, 0, 1, 2,

-3, -2, -1, 0, 1, 2, 3,

...

The sequence of fractions A196199/A004737 = 0/1, -1/1, 0/2, 1/1, -2/1, -1/2, 0/3, 1/2, 2/1, -3/1, -2/2, -1/3, 0/4, 1/3, 2/2, 3/1, -4/4. -3/2, ... contains every rational number (infinitely ofter) [Laczkovich]. - N. J. A. Sloane, Oct 09 2013

PROG

(PARI) r=[]; for(k=0, 8, r=concat(r, vector(2*k+1, j, j-k-1))); r

(Haskell)

a196199 n k = a196199_row n !! k

a196199_tabf = map a196199_row [0..]

a196199_row n = [-n..n]

b196199 = bFile' "A196199" (concat $ take 101 a196199_tabf) 0

-- Reinhard Zumkeller, Sep 30 2011

CROSSREFS

Cf. absolute values A053615, A002262, A002260, row lengths A005408, row sums A000004, A071797.

Cf. A004737.

Sequence in context: A116433 A106509 A228110 * A053615 A002819 A037834

Adjacent sequences:  A196196 A196197 A196198 * A196200 A196201 A196202

KEYWORD

sign,tabf,easy,frac,look

AUTHOR

Franklin T. Adams-Watters, Sep 29 2011

STATUS

approved

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Last modified October 20 04:51 EDT 2014. Contains 248329 sequences.