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

3,5

Comments

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

Deleting column 1 of the array at A055126 gives the array A051778 in square format (see Example). - Clark Kimberling, Feb 04 2016

Links

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

Example

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

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 *)

Prog

(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

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).

Sequence in context: A000989 A132401 A104273 * A057554 A060575 A236074

Adjacent sequences: A051775 A051776 A051777 * A051779 A051780 A051781

Keyword

easy,nice,nonn,tabl

Author

Asher Auel, Dec 09 1999

Status

approved