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A194896
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(8).
4
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 7, 2, 3, 4, 5, 6, 1, 7, 2, 8, 3, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 13, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7
OFFSET
1,3
COMMENTS
See A194832 for a general discussion.
EXAMPLE
First nine rows:
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
6 1 2 3 4 5
6 1 7 2 3 4 5
6 1 7 2 8 3 4 5
6 1 7 2 8 3 9 4 5
MATHEMATICA
r = -Sqrt[8];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194896 *)
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},
{k, 1, n}]] (* A194897 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194898 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 04 2011
STATUS
approved