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A096008 Irregular triangle read by rows where n-th row contains all quadratic residues (including zero) mod n. 38
0, 0, 1, 0, 1, 0, 1, 0, 1, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 4, 0, 1, 4, 7, 0, 1, 4, 5, 6, 9, 0, 1, 3, 4, 5, 9, 0, 1, 4, 9, 0, 1, 3, 4, 9, 10, 12, 0, 1, 2, 4, 7, 8, 9, 11, 0, 1, 4, 6, 9, 10, 0, 1, 4, 9, 0, 1, 2, 4, 8, 9, 13, 15, 16, 0, 1, 4, 7, 9, 10, 13, 16, 0, 1, 4, 5, 6, 7, 9, 11, 16, 17, 0, 1, 4, 5, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

T. D. Noe, Rows n = 1..100, flattened

Eric Weisstein's World of Mathematics, Quadratic Residue.

EXAMPLE

The table starts:

[0]

[0, 1]

[0, 1]

[0, 1]

[0, 1, 4]

[0, 1, 3, 4]

[0, 1, 2, 4]

[0, 1, 4]

[0, 1, 4, 7]

[0, 1, 4, 5, 6, 9]

...

MAPLE

q:=n-> sort(convert({seq(i^2 mod n, i=0..n-1)}, list)); # N. J. A. Sloane, Feb 09 2011

MATHEMATICA

row[n_] := Table[PowerMod[k, 2, n], {k, 0, n-1}] // Union; Table[row[n], {n, 1, 20}] // Flatten (* Jean-Fran├žois Alcover, Sep 09 2013 *)

PROG

(PARI) T(n) = {local(v, r, i, j, k); v=vector(n, i, 0); for(i=0, floor(n/2), v[i^2%n+1]=1); k=sum(i=1, n, v[i]); j=0; r=vector(k); for(i=1, n, if(v[i], j++; r[j]=i-1)); r}

(Haskell)

a096008 n k = a096008_tabf !! (n-1) !! (k-1)

a096008_row n = a096008_tabf !! (n-1)

a096008_tabf = [0] : map (0 :) a046071_tabf

-- Reinhard Zumkeller, May 10 2015

CROSSREFS

Cf. A046071 (without zeros), A000224 (row lengths), A063987.

Last elements of rows give A047210.

Row sums give A165909.

Sequence in context: A298063 A298712 A127538 * A122873 A221275 A176803

Adjacent sequences:  A096005 A096006 A096007 * A096009 A096010 A096011

KEYWORD

easy,tabf,nonn

AUTHOR

Cino Hilliard, Jul 20 2004

EXTENSIONS

Edited by Franklin T. Adams-Watters, Nov 07 2006

STATUS

approved

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Last modified October 20 17:50 EDT 2019. Contains 328268 sequences. (Running on oeis4.)