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A292964 Rectangular array by antidiagonals: T(n,m) = rank of n*(1/e + m) when all the numbers k*(1/e+h), for k>=1, h>=0, are jointly ranked.

%I A292964 #4 Oct 05 2017 21:29:39
%S A292964 1,4,2,8,10,3,13,19,16,5,17,29,32,23,6,22,40,48,44,30,7,27,52,65,68,
%T A292964 58,37,9,34,63,82,93,89,72,46,11,38,76,102,118,120,108,87,53,12,43,88,
%U A292964 123,144,153,149,132,101,60,14,50,99,141,171,187,189,178,155
%N A292964 Rectangular array by antidiagonals:  T(n,m) = rank of n*(1/e + m) when all the numbers k*(1/e+h), for k>=1, h>=0, are jointly ranked.
%C A292964 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%H A292964 Clark Kimberling, <a href="/A292964/b292964.txt">Antidiagonals n=1..60, flattened</a>
%F A292964 T(n,m) = Sum_{k=1...[n + m*n*e]} [1 - 1/e + n*(1/e + m)/k], where [ ]=floor.
%e A292964 Northwest corner:
%e A292964 1      4     8      13     17     22
%e A292964 2     10     19     29     40     52
%e A292964 3     16     32     48     65     82
%e A292964 5     23     44     68     93     118
%e A292964 6     30     58     89     120    153
%e A292964 7     37     72     108    149    189
%e A292964 9     46     87     132    178    228
%e A292964 The numbers k*(1/e+h), approximately:
%e A292964 (for k=1):   0.367   1.367  2.3667 ...
%e A292964 (for k=2):   0.735   2.735  4.735 ...
%e A292964 (for k=3):   1.103   4.103  7.103 ...
%e A292964 Replacing each by its rank gives
%e A292964 1    4     8
%e A292964 2    10    19
%e A292964 3    16    32
%t A292964 r = 1/E; z = 12;
%t A292964 t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];
%t A292964 u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u]  (* A292964 array *)
%t A292964 Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292964 sequence *)
%Y A292964 Cf. A182801, A292963.
%K A292964 nonn,easy,tabl
%O A292964 1,2
%A A292964 _Clark Kimberling_, Oct 05 2017