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.
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
Examples
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
Links
- Clark Kimberling, Antidiagonals n=1..60, flattened
Programs
Formula
T(n,m) = Sum_{k=1...[n + m*n/e]} [1 - e + n*(e + m)/k], where [ ]=floor.
Comments