A194836 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194835; an interspersion.

1, 3, 2, 5, 4, 6, 9, 7, 10, 8, 13, 11, 14, 12, 15, 19, 16, 20, 17, 21, 18, 26, 23, 27, 24, 28, 25, 22, 33, 30, 35, 31, 36, 32, 29, 34, 42, 38, 44, 40, 45, 41, 37, 43, 39, 51, 47, 53, 49, 55, 50, 46, 52, 48, 54, 62, 57, 64, 59, 66, 61, 56, 63, 58, 65, 60, 74, 69, 76

Offset: 1

Author

Clark Kimberling, Sep 03 2011

Keywords

• nonn
• tabl

Comments

Each pair of rows eventually intersperse.

Examples

			 Northwest corner:
1...3...5...9...13..19..26
2...4...7...11..16..23..30
6...10..14..20..27..35..44
8...12..17..24..31..40..49
15..21..28..36..45..55..66
18..25..32..41..50..61..73
		

Crossrefs

Cf. A194835, A194837, A194832.

Programs

Mathematica

r = -Sqrt[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}]]  (* A194835 *)
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}]] (* A194836 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
 {n, 1, 80}]]  (* A194837 *)