A332529 - OEIS

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

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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):

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

EXTENSIONS

Definition corrected by Harvey P. Dale, Jun 14 2022

STATUS

approved