proposed

approved

editing

proposed

Then R(n,k) is the rank of T(n,k) when all the numbers in {T(n,k})} are jointly ranked. - Clark Kimberling, Jan 25 2018

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

Rank array R of 3/2 read by antidiagonals; this array is the dispersion of the complement of the sequence given by r(n) = r(n-1) + 1 + [floor(3n/2] ) for n>=1, with r(0) = 1; that is, A077043(n+1).

The sequence is a permutation of the natural numbers positive integers and the array is a transposable dispersion.

1 2 4 8 16 32

3 6 12 24 48 96

9 18 36 72 144 288

27 54 108 216 432 864

1 ... 2 ... 4 ... 6 ... 9 ... 13 .. 17 .. 22

3 ... 5 ... 8 ... 11 .. 15 .. 20 .. 25 .. 31

7 ... 10 .. 14 .. 18 .. 23 .. 29 .. 35 .. 42

12 .. 16 .. 21 .. 26 .. 32 .. 39 .. 46 .. 54

19 .. 24 .. 30 .. 36 .. 43 .. 51 .. 59 .. 68

27 .. 33 .. 40 .. 47 .. 55 .. 64 .. 73 .. 83

37 .. 44 .. 52 .. 60 .. 69 .. 79 .. 89 .. 100

TableForm[Table[w[i, j], {i, 1, 10}, {j, 1, 10}]] (* A087465 array *)

Flatten[Table[w[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A087465 sequence *)

TableForm[Table[w[i, 1] + w[1, j] + (i - 1)*(j - 1) - 1, {i, 1, 10}, {j, 1, 10}]] (* A087465 array, by formula *)

proposed

editing

editing

proposed

Let T(n,k) be the rectangular version of the array at A036561, with northwest corner as shown here:

1 2 4 8 16 32

3 6 12 24 48 96

9 18 36 72 144 288

27 54 108 216 432 864

Then R(n,k) is the rank of T(n,k) when all the numbers in {T(n,k}} are jointly ranked. - Clark Kimberling, Jan 25 2018

approved

editing

proposed

approved