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A332529 Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = 1+ golden ratio = (1+sqrt(5))/2. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..70.

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A001950, A054770, A214971, A284624.

Sequence in context: A197387 A171177 A171176 * A213849 A067418 A287548

Adjacent sequences:  A332526 A332527 A332528 * A332530 A332531 A332532

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Jun 15 2020

STATUS

approved

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Last modified November 29 06:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)