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A332502
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Rectangular array read by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
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1
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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
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OFFSET
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0,4
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COMMENTS
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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.
Main Diagonal: Upper Wythoff sequence, A001950.
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LINKS
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FORMULA
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T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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