A194875 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194874; an interspersion.

1, 3, 2, 5, 4, 6, 9, 7, 10, 8, 13, 11, 14, 12, 15, 19, 16, 20, 17, 21, 18, 25, 22, 26, 23, 27, 24, 28, 33, 29, 34, 30, 35, 31, 36, 32, 41, 37, 42, 38, 43, 39, 44, 40, 45, 51, 46, 52, 47, 53, 48, 54, 49, 55, 50, 62, 57, 63, 58, 64, 59, 65, 60, 66, 61, 56, 73, 68, 75

Offset: 1

Author

Clark Kimberling, Sep 04 2011

Keywords

• nonn
• tabl

Comments

See A194832 for a general discussion.

Examples

			Northwest corner:
1...3...5...9...13..19
2...4...7...11..16..22
6...10..14..20..26..34
8...12..17..23..30..38
15..21..27..35..43..53
		

Crossrefs

Cf. A194832, A194874, A194876.

Programs

Mathematica

r = -Sqrt[6];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194874 *)
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}]]   (* A194875 *)
q[n_] := Position[p, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A194876 *)