A051778 Triangle read by rows, where row (n) = n mod (n-1), n mod (n-2), n mod (n-3), ...n mod 2.

1, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 3, 1, 1, 1, 2, 3, 0, 2, 0, 1, 2, 3, 4, 1, 0, 1, 1, 2, 3, 4, 0, 2, 1, 0, 1, 2, 3, 4, 5, 1, 3, 2, 1, 1, 2, 3, 4, 5, 0, 2, 0, 0, 0, 1, 2, 3, 4, 5, 6, 1, 3, 1, 1, 1, 1, 2, 3, 4, 5, 6, 0, 2, 4, 2, 2, 0, 1, 2, 3, 4, 5, 6, 7, 1, 3, 0, 3, 0, 1, 1, 2, 3, 4, 5, 6, 7, 0, 2, 4, 1, 0, 1, 0

Offset: 3

Author

Asher Auel, Dec 09 1999

Keywords

• easy
• nice
• nonn
• tabl

Comments

Central terms: a(2*n+1,n) = n for n > 0. - Reinhard Zumkeller, Dec 03 2014

Deleting column 1 of the array at A051126 gives the array A051778 in square format (see Example). - Clark Kimberling, Feb 04 2016

Examples

			row (7) = 7 mod 6, 7 mod 5, 7 mod 4, 7 mod 3, 7 mod 2 = 1, 2, 3, 1, 1.
1;
1  0 ;
1  2  1 ;
1  2  0  0 ;
1  2  3  1  1 ;
1  2  3  0  2  0 ;
1  2  3  4  1  0  1 ;
1  2  3  4  0  2  1  0 ;
1  2  3  4  5  1  3  2  1 ;
1  2  3  4  5  0  2  0  0  0 ;
1  2  3  4  5  6  1  3  1  1  1 ;
Northwest corner of square array:
1 1 1 1 1 1 1 1 1 1 1
0 2 2 2 2 2 2 2 2 2 2
1 0 3 3 3 3 3 3 3 3 3
0 1 0 4 4 4 4 4 4 4 4
1 2 1 0 5 5 5 5 5 5 5
0 0 2 1 0 6 6 6 6 6 6
1 1 3 2 1 0 7 7 7 7 7
- _Clark Kimberling_, Feb 04 2016
		

Links

• Reinhard Zumkeller, Rows n=3..125 of triangle, flattened

Crossrefs

Cf. A051777, A051127, A051126.

Cf. A004125 (row sums), A000027 (central terms), A049820 (number of nonzeros per row), A032741 (number of ones per row), A070824 (number of zeros per row).

Programs

Haskell

a051778 n k = a051778_tabl !! (n-3) !! (k-1)
a051778_row n = a051778_tabl !! (n-3)
a051778_tabl = map (\xs -> map (mod (head xs + 1)) xs) $
                   iterate (\xs -> (head xs + 1) : xs) [2]
-- Reinhard Zumkeller, Dec 03 2014

Mathematica

Flatten[Table[Mod[n,i],{n,3,20},{i,n-1,2,-1}]] (* Harvey P. Dale, Sep 09 2012 *)
TableForm[Table[Mod[n, k], {n, 1, 12}, {k, 2, 12}]] (* square *)
(* Clark Kimberling, Feb 04 2016 *)