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A332529
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Rectangular array 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, 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
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0,2
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COMMENTS
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Column 0: Nonnegative integers.
Row 0: Upper Wythoff sequence, A001950, with 0 prepended.
Main Diagonal: A003231, with 0 prepended.
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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)^2 = (3+sqrt(5))/2.
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EXAMPLE
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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
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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}]] (* A332529 array *)
Table[t[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* A332529 sequence *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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