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/r]} [1 - r + n*(r + m)/k], where r=(GoldenRatio)^2 and [ ]=floor.
EXAMPLE
Northwest corner:
1 2 3 5 6 8 10
4 7 11 16 20 25 30
9 15 22 29 38 46 55
13 23 34 44 57 69 83
19 32 47 62 78 95 112
27 43 61 81 102 122 145
The numbers k*(r+h), approximately:
(for k=1): 2.618 3.618 4.618 ...
(for k=2): 5.236 7.236 9.236 ...
(for k=3): 7.854 10.854 13.854 ...
Replacing each k*(r+h) by its rank gives
1 2 3
4 7 11
9 15 22
MATHEMATICA
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 05 2017
STATUS
approved