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
Examples
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 ...
Links
- Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
Programs
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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 *) -
PARI
T(n, k)=k%n \\ Charles R Greathouse IV, Feb 09 2017
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
Extensions
More terms from James Sellers, Dec 11 1999
Comments