A194878 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194877; an interspersion.

1, 3, 2, 6, 5, 4, 10, 9, 8, 7, 15, 14, 13, 12, 11, 20, 19, 18, 17, 16, 21, 27, 25, 24, 23, 22, 28, 26, 35, 33, 31, 30, 29, 36, 34, 32, 44, 42, 40, 38, 37, 45, 43, 41, 39, 54, 52, 50, 48, 46, 55, 53, 51, 49, 47, 65, 63, 61, 59, 57, 66, 64, 62, 60, 58, 56, 76, 74, 72

Offset: 1

Author

Clark Kimberling, Sep 04 2011

Keywords

• nonn
• tabl

Comments

See A194832 for a general discussion.

Examples

			Northwest corner:
1...3...6...10..15..20..27
2...5...9...14..19..25..33
4...8...13..18..24..31..40
7...12..17..23..30..38..48
11..16..22..29..37..46..57
		

Crossrefs

Cf. A194832, A194877, A194879.

Programs

Mathematica

r = Sqrt[8];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]   (* A194877 *)
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}]]   (* A194878 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A194879 *)