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A332502
Rectangular array read by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
1
0, 1, 1, 3, 2, 2, 4, 4, 3, 3, 6, 5, 5, 4, 4, 8, 7, 6, 6, 5, 5, 9, 9, 8, 7, 7, 6, 6, 11, 10, 10, 9, 8, 8, 7, 7, 12, 12, 11, 11, 10, 9, 9, 8, 8, 14, 13, 13, 12, 12, 11, 10, 10, 9, 9, 16, 15, 14, 14, 13, 13, 12, 11, 11, 10, 10, 17, 17, 16, 15, 15, 14, 14, 13
OFFSET
0,4
COMMENTS
Every nonnegative integer occurs exactly once in the union of row 0 and the main diagonal.
Column 0: Nonnegative integers, A001477.
Row 0: Lower Wythoff sequence, A000201.
Row 1: A026351.
Row 2: A026355 (and essentially A099267).
Main Diagonal: Upper Wythoff sequence, A001950.
Diagonal (1,4,6,9,...) = A003622;
Diagonal (3,5,8,11,...) = A026274;
Diagonal (1,3,6,8,...) = A026352;
Diagonal (2,4,7,9,...) = A026356.
FORMULA
T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
EXAMPLE
Northwest corner:
0 1 3 4 6 8 9 11 12 14 16
1 2 4 5 7 9 10 12 13 15 17
2 3 5 6 8 10 11 13 14 16 18
3 4 6 7 9 11 12 14 15 17 19
4 5 7 8 10 12 13 15 16 18 20
5 6 8 9 11 13 14 16 17 19 21
As a triangle (antidiagonals):
0
1 1
2 2 3
3 3 4 4
4 4 5 5 6
5 5 6 6 7 8
6 6 7 7 8 9 9
MATHEMATICA
t[n_, k_] := Floor[n + k*GoldenRatio];
Grid[Table[t[n, k], {n, 0, 10}, {k, 0, 10}]] (* array *)
u = Table[t[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* sequence *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, May 08 2020
STATUS
approved