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 A293054 #6 Oct 06 2017 21:34:38
%S A293054 1,2,4,3,6,9,5,8,12,16,7,11,15,20,25,10,14,19,24,30,37,13,18,23,29,35,
%T A293054 43,51,17,22,28,34,41,49,58,67,21,27,33,40,47,56,65,75,85,26,32,39,46,
%U A293054 54,63,73,83,94,106,31,38,45,53,61,71,81,92,103,116,129
%N A293054 Rectangular array by antidiagonals: T(n,m) = rank of n*sqrt(5)+m when all the numbers k*sqrt(5)+h, for k >= 1, h >= 0, are jointly ranked.
%C A293054 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. As an array, this is the interspersion of sqrt(1/5); see A283962.
%H A293054 Clark Kimberling, <a href="/A293054/b293054.txt">Antidiagonals n=1..60, flattened</a>
%F A293054 T(n,m) = Sum_{k=1...n + [m/r]} m+1+[(n-k)r], where r = sqrt(5), [ ]=floor.
%e A293054 Northwest corner:
%e A293054 1 2 3 5 7 10 13
%e A293054 4 6 8 11 14 18 22
%e A293054 9 12 15 19 23 28 33
%e A293054 16 20 24 29 34 40 46
%e A293054 25 30 35 41 47 54 61
%e A293054 37 43 49 56 63 71 79
%e A293054 51 58 65 73 81 90 99
%e A293054 67 75 83 92 101 111 121
%e A293054 85 94 103 113 123 134 145
%e A293054 The numbers k*r+h, approximately:
%e A293054 (for k=1): 2.236 3.236 3.236 ...
%e A293054 (for k=2): 4.472 5.472 6.472 ...
%e A293054 (for k=3): 6.708 7.708 8.708 ...
%e A293054 Replacing each k*r+h by its rank gives
%e A293054 1 2 3
%e A293054 4 6 8
%e A293054 9 12 15
%t A293054 r = Sqrt[5]; z = 12;
%t A293054 t[n_, m_] := Sum[Floor[1 + m + (n - k) r], {k, 1, n + Floor[m/r]}];
%t A293054 u = Table[t[n, m], {n, 1, z}, {m, 0, z}]
%t A293054 Grid[u] (* A293054 array *)
%t A293054 Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A293054 sequence *)
%Y A293054 Cf. A283962.
%K A293054 nonn,easy,tabl
%O A293054 1,2
%A A293054 _Clark Kimberling_, Oct 06 2017