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 A368434 #5 Dec 30 2023 23:41:21
%S A368434 1,2,4,2,3,8,10,4,2,4,12,18,16,8,4,2,5,16,26,28,24,12,8,4,2,6,20,34,
%T A368434 40,40,32,18,12,8,4,2,7,24,42,52,56,52,42,24,18,12,8,4,2,8,28,50,64,
%U A368434 72,72,66,52,32,24,18,12,8,4,2,9,32,58,76,88,92,90,80
%N A368434 Irregular triangular array T, read by rows: T(n,k) = number of sums |x-y|+|y-z| = k, where x,y,z are in {0,1,...,n}.
%C A368434 Row n consists of 2n-1 positive integers having sum A000575(n) = n^3.
%e A368434 First eight rows:
%e A368434 1
%e A368434 2 4 2
%e A368434 3 8 10 4 2
%e A368434 4 12 18 16 8 4 2
%e A368434 5 16 26 28 24 12 8 4 2
%e A368434 6 20 34 40 40 32 18 12 8 4 2
%e A368434 7 24 42 52 56 52 42 24 18 12 8 4 2
%e A368434 8 28 50 64 72 72 66 52 32 24 18 12 8 4 2
%t A368434 t[n_] := t[n] = Tuples[Range[n], 3];
%t A368434 a[n_, k_] := Select[t[n], Abs[#[[1]] - #[[2]]] + Abs[#[[2]] - #[[3]]] == k &];
%t A368434 u = Table[Length[a[n, k]], {n, 1, 15}, {k, 0, 2 n - 2}];
%t A368434 Flatten[u] (* sequence *)
%t A368434 Column[u] (* array *)
%Y A368434 Cf. A000575, A007590 (limiting reversed row), A368435 (reversed rows), A368435, A368346.
%K A368434 nonn,tabf
%O A368434 1,2
%A A368434 _Clark Kimberling_, Dec 25 2023