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A051127
Table T(n,k) = k mod n read by antidiagonals (n >= 1, k >= 1).
13
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
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
G.f. for the n-th row: y*Sum_{i=0..n-2} (i + 1)*y^i/(1 - y^n). - Stefano Spezia, May 08 2024
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.
Sequence in context: A227834 A025894 A339087 * A070176 A092606 A374133
KEYWORD
nonn,tabl,easy,nice
EXTENSIONS
More terms from James A. Sellers, Dec 11 1999
STATUS
approved