This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051126 #32 Jul 02 2025 16:01:58
%S A051126 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,
%T A051126 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,
%U A051126 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
%N A051126 Table T(n,k) = n mod k read by downward antidiagonals (n >= 1, k >= 1).
%H A051126 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A051126 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
%F A051126 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
%e A051126 Table begins in row n=1:
%e A051126 0 1 1 1 1 1 1 1 1 1 ...
%e A051126 0 0 2 2 2 2 2 2 2 2 ...
%e A051126 0 1 0 3 3 3 3 3 3 3 ...
%e A051126 0 0 1 0 4 4 4 4 4 4 ...
%e A051126 0 1 2 1 0 5 5 5 5 5 ...
%e A051126 0 0 0 2 1 0 6 6 6 6 ...
%e A051126 0 1 1 3 2 1 0 7 7 7 ...
%e A051126 0 0 2 0 3 2 1 0 8 8 ...
%e A051126 0 1 0 1 4 3 2 1 0 9 ...
%e A051126 0 0 1 2 0 4 3 2 1 0 ...
%e A051126 0 1 2 3 1 5 4 3 2 1 ...
%e A051126 0 0 0 0 2 0 5 4 3 2 ...
%e A051126 0 1 1 1 3 1 6 5 4 3 ...
%t A051126 TableForm[Table[Mod[n, k], {n, 1, 16}, {k, 1, 16}]] (* A051126 array *)
%t A051126 Table[Mod[n - k + 1, k], {n, 16}, {k, n, 1, -1}] // Flatten (* A051126 sequence *)
%t A051126 (* _Clark Kimberling_, Feb 04 2016 *)
%Y A051126 Cf. A051127, A048158, A051777, A051778.
%Y A051126 Cf. A002260, A004736.
%K A051126 nonn,tabl,easy,nice
%O A051126 1,8
%A A051126 _N. J. A. Sloane_
%E A051126 More terms from _James Sellers_, Dec 11 1999