A194863 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194862; an interspersion.

1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 12, 14, 11, 13, 15, 18, 20, 16, 19, 21, 17, 24, 27, 22, 25, 28, 23, 26, 31, 34, 29, 32, 35, 30, 33, 36, 40, 43, 37, 41, 44, 38, 42, 45, 39, 49, 53, 46, 50, 54, 47, 51, 55, 48, 52, 60, 64, 57, 61, 65, 58, 62, 66, 59, 63, 56, 71, 76, 68

Offset: 1

Author

Clark Kimberling, Sep 04 2011

Keywords

• nonn
• tabl

Comments

For a general discussion, see A194832.

Examples

			Northwest corner:
1...2...5...8...12..18
3...6...10..14..20..27
4...7...11..16..22..29
9...13..19..25..32..41
15..21..28..35..44..54
		

Crossrefs

Cf. A194832, A194862, A194867.

Programs

Mathematica

r = (1 + Sqrt[3])/2;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194862 *)
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}]]  (* A194863 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194867 *)