A051127 - OEIS

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

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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

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 ...