A051777 Triangle read by rows, where row (n) = n mod n, n mod (n-1), n mod (n-2), ...n mod 1.

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

Offset

1,13

Comments

Also, rectangular array read by antidiagonals, a(n, k) = k mod n (k >= 0, n >= 1). Cf. A048158, A051127. - David Wasserman, Oct 01 2008

Central terms: a(2*n - 1, n) = n - 1. - Reinhard Zumkeller, Jan 25 2011

Links

Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Example

row (5) = 5 mod 5, 5 mod 4, 5 mod 3, 5 mod 2, 5 mod 1 = 0, 1, 2, 1, 0.
0 ;
0  0 ;
0  1  0 ;
0  1  0  0 ;
0  1  2  1  0;
0  1  2  0  0  0 ;
0  1  2  3  1  1  0 ;
0  1  2  3  0  2  0  0;
0  1  2  3  4  1  0  1  0 ;
0  1  2  3  4  0  2  1  0  0 ;
0  1  2  3  4  5  1  3  2  1  0 ;
0  1  2  3  4  5  0  2  0  0  0  0 ;
0  1  2  3  4  5  6  1  3  1  1  1  0 ;

Mathematica

Flatten[Table[Mod[n, Range[n, 1, -1]], {n, 20}]] (* Harvey P. Dale, Nov 30 2011 *)

Prog

(Haskell)
a051777 n k = a051777_row n !! (k-1)
a051777_row n = map (mod n) [n, n-1 .. 1]
a051777_tabl = map a051777_row [1..]
-- Reinhard Zumkeller, Jan 25 2011

Crossrefs

Cf. A051778. Row sums give A004125. Number of 0's in row n gives A000005 (tau(n)). Number of 1's in row n+1 gives A032741(n).

Sequence in context: A035468 A369311 A263860 * A262709 A107628 A268389

Adjacent sequences: A051774 A051775 A051776 * A051778 A051779 A051780

Keyword

easy,nice,nonn,tabl

Author

Asher Auel, Dec 09 1999

Status

approved