A051127 Table T(n,k) = k mod n read by antidiagonals (n >= 1, k >= 1).

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

Offset

1,9

Comments

Note that the upper right half of this sequence when formatted as a square array is essentially the same as this whole sequence when formatted as an upper right triangle. Sums of antidiagonals are A004125. - Henry Bottomley, Jun 22 2001

Links

Table of n, a(n) for n=1..105.

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

As a linear array, the sequence is a(n) = A004736(n) mod A002260(n) or a(n) = ((t*t+3*t+4)/2-n) mod (n-(t*(t+1)/2)), where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 17 2012

Example

0  0  0  0  0  0  0  0  0  0 ...
1  0  1  0  1  0  1  0  1  0 ...
1  2  0  1  2  0  1  2  0  1 ...
1  2  3  0  1  2  3  0  1  2 ...
1  2  3  4  0  1  2  3  4  0 ...
1  2  3  4  5  0  1  2  3  4 ...
1  2  3  4  5  6  0  1  2  3 ...
1  2  3  4  5  6  7  0  1  2 ...
1  2  3  4  5  6  7  8  0  1 ...
1  2  3  4  5  6  7  8  9  0 ...
1  2  3  4  5  6  7  8  9 10 ...
1  2  3  4  5  6  7  8  9 10 ...
1  2  3  4  5  6  7  8  9 10 ...

Mathematica

T[n_, m_] = Mod[n - m + 1, m + 1]; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] (* Roger L. Bagula, Sep 04 2008 *)

Prog

(PARI) T(n, k)=k%n \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Transpose of A051126.

Cf. A048158, A051777, A122750.

Sequence in context: A227834 A025894 A339087 * A070176 A092606 A275948

Adjacent sequences: A051124 A051125 A051126 * A051128 A051129 A051130

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 11 1999

Status

approved