A051126 - OEIS

A051126

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

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

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OFFSET

1,8

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) = A002260(n) mod A004736 (n) or a(n) = (n-(t*(t+1)/2)) mod ((t*t+3*t+4)/2-n), where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 19 2012

G.f. of the k-th column: x*Sum_{i=0..k-2} (i + 1)*x^i/(1 - x^k). - Stefano Spezia, May 08 2024

EXAMPLE

Table begins in row n=1:

0 1 1 1 1 1 1 1 1 1 ...

0 0 2 2 2 2 2 2 2 2 ...

0 1 0 3 3 3 3 3 3 3 ...

0 0 1 0 4 4 4 4 4 4 ...

0 1 2 1 0 5 5 5 5 5 ...

0 0 0 2 1 0 6 6 6 6 ...

0 1 1 3 2 1 0 7 7 7 ...

0 0 2 0 3 2 1 0 8 8 ...

0 1 0 1 4 3 2 1 0 9 ...