A194903 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194902; 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, 61, 56, 62, 57, 63, 58, 64, 59, 65, 60, 66, 73, 67, 74

Offset

1,2

Comments

See A194832 for a general discussion.

Links

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

Example

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

Mathematica

r = -Sqrt[12];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1,
    20}]] (* A194902 *)
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}]] (* A194903 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194904 *)

Crossrefs

Cf. A194832, A194902, A194903.

Sequence in context: A355014 A302252 A176988 * A194875 A194836 A054069

Adjacent sequences: A194900 A194901 A194902 * A194904 A194905 A194906

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 05 2011

Status

approved