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A194856
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Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-sqrt(5).
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4
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1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 6, 1, 5, 4, 3, 7, 2, 6, 1, 5, 4, 8, 3, 7, 2, 6, 1, 5, 4, 8, 3, 7, 2, 6, 1, 5, 9, 4, 8, 3, 7, 2, 6, 10, 1, 5, 9, 4, 8, 3, 7, 11, 2, 6, 10, 1, 5, 9, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 13, 4, 8, 12
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OFFSET
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1,2
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COMMENTS
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See A194832 for a general discussion.
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LINKS
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EXAMPLE
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First nine rows:
1
2 1
3 2 1
4 3 2 1
4 3 2 1 5
4 3 2 6 1 5
4 3 7 2 6 1 5
4 8 3 7 2 6 1 5
4 8 3 7 2 6 1 5 9
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MATHEMATICA
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r = -Sqrt[5];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194856 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
q[n_] := Position[p, n]; Flatten[Table[q[n],
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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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