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.
The top left 9 X 9 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...): 0 5 6 47 48 53 54 59 60 1 4 7 46 49 52 55 58 61 2 3 8 45 50 51 56 57 62 15 14 9 44 39 38 69 68 63 16 13 10 43 40 37 70 67 64 17 12 11 42 41 36 71 66 65 18 23 24 29 30 35 72 77 78 19 22 25 28 31 34 73 76 79 20 21 26 27 32 33 74 75 80
b[{n_, k_}, {m_}] := (A[n, k] = m - 1);
MapIndexed[b, List @@ PeanoCurve[4][[1]]];
Table[A[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)
From _Kevin Ryde_, Oct 06 2020: (Start)
Array A(y,x) read by downwards antidiagonals, so 0, 1,3, 2,4,6, etc.
x=0 1 2 3 4 5 6 7 8
+--------------------------------------
y=0 | 0, 1, 2, 9, 10, 11, 18, 19, 20,
1 | 3, 4, 5, 12, 13, 14, 21, 22,
2 | 6, 7, 8, 15, 16, 17, 24,
3 | 27, 28, 29, 36, 37, 38,
4 | 30, 31, 32, 39, 40,
5 | 33, 34, 35, 42,
6 | 54, 55, 56,
7 | 57, 58,
8 | 60,
(End)