A194897 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194896; an interspersion.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 16, 23, 25, 26, 27, 28, 22, 24, 30, 32, 34, 35, 36, 29, 31, 33, 38, 40, 42, 44, 45, 37, 39, 41, 43, 47, 49, 51, 53, 55, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 56, 58, 60, 62, 64, 66, 69, 71, 73

Offset

1,2

Comments

See A194832 for a general discussion.

Links

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

Example

Northwest corner:
1...2...4...7...11..17..23
3...5...8...12..18..25..32
6...9...13..19..26..34..42
10..14..20..27..35..44..53
15..21..28..36..45..55..65
16..22..29..37..46..56..67

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}]] (* A194896 *)
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}]] (* A194897 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A194898 *)

Crossrefs

Cf. A194832, A194896, A194898.

Sequence in context: A023797 A032951 A288139 * A140823 A209061 A115063

Adjacent sequences: A194894 A194895 A194896 * A194898 A194899 A194900

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 04 2011

Status

approved