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A292964
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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.
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2
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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, 58, 37, 9, 34, 63, 82, 93, 89, 72, 46, 11, 38, 76, 102, 118, 120, 108, 87, 53, 12, 43, 88, 123, 144, 153, 149, 132, 101, 60, 14, 50, 99, 141, 171, 187, 189, 178, 155
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OFFSET
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1,2
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COMMENTS
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Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
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LINKS
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Clark Kimberling, Antidiagonals n=1..60, flattened
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FORMULA
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T(n,m) = Sum_{k=1...[n + m*n*e]} [1 - 1/e + n*(1/e + m)/k], where [ ]=floor.
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EXAMPLE
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Northwest corner:
1 4 8 13 17 22
2 10 19 29 40 52
3 16 32 48 65 82
5 23 44 68 93 118
6 30 58 89 120 153
7 37 72 108 149 189
9 46 87 132 178 228
The numbers k*(1/e+h), approximately:
(for k=1): 0.367 1.367 2.3667 ...
(for k=2): 0.735 2.735 4.735 ...
(for k=3): 1.103 4.103 7.103 ...
Replacing each by its rank gives
1 4 8
2 10 19
3 16 32
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MATHEMATICA
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r = 1/E; z = 12;
t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];
u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u] (* A292964 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A292964 sequence *)
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CROSSREFS
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Cf. A182801, A292963.
Sequence in context: A125065 A109816 A296477 * A050128 A321119 A246202
Adjacent sequences: A292961 A292962 A292963 * A292965 A292966 A292967
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Clark Kimberling, Oct 05 2017
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STATUS
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approved
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