A332529 Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.

0, 2, 1, 5, 3, 2, 7, 6, 4, 3, 10, 8, 7, 5, 4, 13, 11, 9, 8, 6, 5, 15, 14, 12, 10, 9, 7, 6, 18, 16, 15, 13, 11, 10, 8, 7, 20, 19, 17, 16, 14, 12, 11, 9, 8, 23, 21, 20, 18, 17, 15, 13, 12, 10, 9, 26, 24, 22, 21, 19, 18, 16, 14, 13, 11, 10, 28, 27, 25, 23, 22

Offset: 0

Author

Clark Kimberling, Jun 15 2020

Keywords

• nonn
• tabl
• easy

Comments

Column 0: Nonnegative integers.

Row 0: Upper Wythoff sequence, A001950, with 0 prepended.

Main Diagonal: A003231, with 0 prepended.

Diagonal (2,6,9,13,...) = A054770.

Diagonal (1,4,8,11,...) = A214971.

Diagonal (2,5,9,12,...) = A284624.

Examples

			Northwest corner:
  0   2    5    7   10   13   15
  1   3    6    8   11   14   16
  2   4    7    9   12   15   17
  3   5    8   10   13   16   18
  4   6    9   11   14   17   19
  5   7   10   12   15   18   20
  6   8   11   13   16   19   21
As a triangle (antidiagonals):
  0
  1   2
  2   3   5
  3   4   6   7
  4   5   7   8  10
		

Crossrefs

Cf. A001950, A054770, A214971, A284624.

Programs

Mathematica

t[n_, k_] := Floor[n + k*GoldenRatio];
Grid[Table[t[n, k], {n, 0, 10}, {k, 0, 10}]] (* A332529 array *)
Table[t[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten  (* A332529 sequence *)

Formula

T(n,k) = floor(n + k*r), where r = (golden ratio)^2 = (3+sqrt(5))/2.

Extensions

Definition corrected by Harvey P. Dale, Jun 14 2022