A194845 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194844; an interspersion.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 11, 17, 19, 20, 21, 16, 18, 23, 25, 27, 28, 22, 24, 26, 30, 32, 34, 36, 29, 31, 33, 35, 39, 41, 43, 45, 38, 40, 42, 44, 37, 48, 51, 53, 55, 47, 50, 52, 54, 46, 49, 58, 61, 64, 66, 57, 60, 63, 65, 56, 59, 62, 69, 72, 75

Offset: 1

Author

Clark Kimberling, Sep 04 2011

Keywords

• nonn
• tabl

Comments

See A194832 and A194844.

Examples

			Northwest corner:
1...2...4...7...12..17
3...5...8...13..19..25
6...9...14..20..27..34
10..15..21..28..36..45
11..16..22..29..38..47
18..24..31..40..50..60
		

Crossrefs

Cf. A194832, A194844, A194846.

Programs

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}]]  (* A194844 *)
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}]]    (* A194845 *)
q[n_] := Position[p, n]; Flatten[
 Table[q[n], {n, 1, 80}]]   (* A194846 *)