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 A322038 #20 Dec 02 2018 05:02:52
%S A322038 1,1,1,2,1,1,4,4,1,4,6,4,1,1,4,8,8,4,1,4,8,10,8,4,1,1,4,8,12,12,8,4,1,
%T A322038 4,8,12,14,12,8,4,1,1,4,8,12,16,16,12,8,4,1,4,8,12,16,18,16,12,8,4,1,
%U A322038 1,4,8,12,16,20,20,16,12,8,4
%N A322038 Irregular triangle read by rows: for n >= 0, row n gives the coordination sequence for the tiling of a flat torus by a square grid with n points along each circuit.
%C A322038 More precisely, this is the coordination sequence for the quotient graph Z^2 / (nZ X nZ). The graph has n^2 vertices.
%C A322038 There are obvious generalizations: for example, Z^2 / (mZ X nZ) where m and n are not necessarily equal.
%H A322038 N. J. A. Sloane, <a href="/A322038/a322038_1.png">Illustration showing the tilings and coordination sequences for n = 4 and 5</a>
%F A322038 Since the underlying graphs are finite, the coordination sequences are polynomial P_n(x).
%F A322038 For n even, P_n(x) = (1+x)^2*(Sum_{i=0..(n-2)/2} x^i)^2;
%F A322038 for n odd, P_n(x) = (1 + 2*Sum_{i=0..(n-1)/2} x^i)^2.
%e A322038 The triangle begins:
%e A322038 1,
%e A322038 1,
%e A322038 1, 2, 1,
%e A322038 1, 4, 4,
%e A322038 1, 4, 6, 4, 1,
%e A322038 1, 4, 8, 8, 4,
%e A322038 1, 4, 8, 10, 8, 4, 1,
%e A322038 1, 4, 8, 12, 12, 8, 4,
%e A322038 1, 4, 8, 12, 14, 12, 8, 4, 1,
%e A322038 1, 4, 8, 12, 16, 16, 12, 8, 4,
%e A322038 1, 4, 8, 12, 16, 18, 16, 12, 8, 4, 1,
%e A322038 ...
%Y A322038 The rows converge to A008574.
%K A322038 nonn,tabf
%O A322038 0,4
%A A322038 _N. J. A. Sloane_, Dec 01 2018