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A292963
Rectangular array by antidiagonals: T(n,m) = rank of n*(e + m) when all the numbers k*(e+h), for k>=1, h>=0, are jointly ranked.
2
1, 2, 4, 3, 7, 9, 5, 11, 15, 14, 6, 16, 22, 24, 20, 8, 19, 29, 34, 32, 27, 10, 25, 38, 45, 48, 43, 35, 12, 30, 46, 57, 62, 61, 54, 42, 13, 36, 55, 70, 79, 81, 76, 67, 50, 17, 40, 64, 83, 95, 101, 100, 92, 78, 58, 18, 47, 73, 97, 113, 122, 125, 120, 108, 89
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
LINKS
FORMULA
T(n,m) = Sum_{k=1...[n + m*n/e]} [1 - e + n*(e + m)/k], where [ ]=floor.
EXAMPLE
Northwest corner:
1 2 3 5 6 8
4 7 11 16 19 25
9 15 22 29 38 46
14 24 34 45 57 70
20 32 48 62 79 95
27 43 61 81 101 122
35 54 76 100 125 152
42 67 92 120 151 181
The numbers k*(r+h), approximately:
(for k=1): 2.718 3.718 4.718 ...
(for k=2): 5.436 7.436 9.436 ...
(for k=3): 8.154 11.854 14.154 ...
Replacing each by its rank gives
1 2 3
4 7 14
9 15 22
MATHEMATICA
r = 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] (* A292963 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A292963 sequence *)
CROSSREFS
Sequence in context: A225010 A235494 A292960 * A262759 A246268 A246267
KEYWORD
nonn,easy,tabl
AUTHOR
Clark Kimberling, Oct 05 2017
STATUS
approved