A194857 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194856; an interspersion.

1, 3, 2, 6, 5, 4, 10, 9, 8, 7, 14, 13, 12, 11, 15, 20, 18, 17, 16, 21, 19, 27, 25, 23, 22, 28, 26, 24, 35, 33, 31, 29, 36, 34, 32, 30, 43, 41, 39, 37, 44, 42, 40, 38, 45, 53, 50, 48, 46, 54, 51, 49, 47, 55, 52, 64, 61, 58, 56, 65, 62, 59, 57, 66, 63, 60, 76, 73, 70

Offset

1,2

Comments

See A194832 for a general discussion.

Links

Table of n, a(n) for n=1..69.

Example

Northwest corner:
1...3...6...10...14...20
2...5...9...13...18...25
4...8...12..17...23...51
7...11..16..22...29...37
15..21..38..36...44...54

Mathematica

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},
 {k, 1, n}]]  (* A194857 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194858 *)

Crossrefs

Cf. A194856, A194858, A194832.

Sequence in context: A194922 A195080 A194858 * A194879 A194878 A194910

Adjacent sequences: A194854 A194855 A194856 * A194858 A194859 A194860

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 04 2011

Status

approved