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 A293052 #6 Oct 06 2017 21:34:29
%S A293052 1,2,3,4,5,7,6,8,10,13,9,11,14,17,20,12,15,18,22,25,29,16,19,23,27,31,
%T A293052 35,40,21,24,28,33,37,42,47,53,26,30,34,39,44,49,55,61,67,32,36,41,46,
%U A293052 51,57,63,70,76,83,38,43,48,54,59,65,72,79,86,93,101,45
%N A293052 Rectangular array by antidiagonals: T(n,m) = rank of n*sqrt(3)+m when all the numbers k*sqrt(3)+h, for k >= 1, h >= 0, are jointly ranked.
%C A293052 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(1/3); see A283962.
%H A293052 Clark Kimberling, <a href="/A293052/b293052.txt">Antidiagonals n=1..60, flattened</a>
%F A293052 T(n,m) = Sum_{k=1...n + [m/r]} m+1+[(n-k)r], where r = sqrt(3), [ ]=floor.
%e A293052 Northwest corner:
%e A293052 1 2 4 6 9 12 16
%e A293052 3 5 8 11 15 19 24
%e A293052 7 10 14 18 23 28 34
%e A293052 13 17 22 27 33 39 46
%e A293052 20 25 31 37 44 51 59
%e A293052 29 35 42 49 57 65 74
%e A293052 40 47 55 63 72 81 91
%e A293052 53 61 70 79 89 99 110
%e A293052 67 76 86 96 107 118 130
%e A293052 The numbers k*r+h, approximately:
%e A293052 (for k=1): 1.732 2.732 3.732 ...
%e A293052 (for k=2): 3.464 4.464 5.464 ...
%e A293052 (for k=3): 5.196 6.196 7.196 ...
%e A293052 Replacing each k*r+h by its rank gives
%e A293052 1 2 4
%e A293052 3 5 8
%e A293052 7 10 14
%t A293052 r = Sqrt[3]; z = 12;
%t A293052 t[n_, m_] := Sum[Floor[1 + m + (n - k) r], {k, 1, n + Floor[m/r]}];
%t A293052 u = Table[t[n, m], {n, 1, z}, {m, 0, z}]
%t A293052 Grid[u] (* A293052 array *)
%t A293052 Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A293052 sequence *)
%Y A293052 Cf. A283962.
%K A293052 nonn,easy,tabl
%O A293052 1,2
%A A293052 _Clark Kimberling_, Oct 06 2017