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