A194869 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194868; an interspersion.

1, 3, 2, 5, 4, 6, 9, 7, 10, 8, 14, 12, 15, 13, 11, 19, 17, 21, 18, 16, 20, 26, 23, 28, 25, 22, 27, 24, 34, 31, 36, 33, 30, 35, 32, 29, 42, 39, 45, 41, 38, 44, 40, 37, 43, 52, 48, 55, 51, 47, 54, 50, 46, 53, 49, 62, 58, 65, 61, 57, 64, 60, 56, 63, 59, 66, 74, 69, 77

Offset

1,2

Comments

Every pair of rows eventually intersperse.

Links

Table of n, a(n) for n=1..69.

Example

Northwest corner:
1...3...5...9...14..19
2...4...7...12..17..23
6...10..15..21..28..36
8...13..18..25..33..41
11..16..22..30..38..47
20..27..35..44..54..64

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}]]  (* A194868 *)
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}]] (* A194869 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A194870 *)

Crossrefs

Cf. A194832, A194868, A194870.

Sequence in context: A194875 A194836 A054069 * A191736 A297208 A301941

Adjacent sequences: A194866 A194867 A194868 * A194870 A194871 A194872

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 04 2011

Status

approved