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.

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

Offset

1,2

Comments

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

Links

Clark Kimberling, Antidiagonals n=1..60, flattened

Formula

T(n,m) = Sum_{k=1...[n + m*n*e]} [1 - 1/e + n*(1/e + m)/k], where [ ]=floor.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A182801, A292963.

Sequence in context: A125065 A109816 A296477 * A050128 A321119 A246202

Adjacent sequences: A292961 A292962 A292963 * A292965 A292966 A292967

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Oct 05 2017

Status

approved