A194981 Interspersion fractally induced by A194979, a rectangular array, by antidiagonals.

1, 2, 3, 4, 6, 5, 7, 10, 8, 9, 11, 15, 12, 14, 13, 16, 21, 17, 20, 18, 19, 22, 28, 23, 27, 24, 25, 26, 29, 36, 30, 35, 31, 32, 34, 33, 37, 45, 38, 44, 39, 40, 43, 41, 42, 46, 55, 47, 54, 48, 49, 53, 50, 52, 51, 56, 66, 57, 65, 58, 59, 64, 60, 63, 61, 62, 67, 78, 68

Offset

1,2

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194981 is a permutation of the positive integers, with inverse A194982.

Links

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

Example

Northwest corner:
1...2...4...7...11..16..22
3...6...10..15..21..28..36
5...8...12..17..23..30..38
9...14..20..27..35..44..54
13..18..24..31..39..48..58

Mathematica

r = Sqrt[3]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194979 = 1+ A097337 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A194980 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]  (* A194981 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194982 *)

Crossrefs

Cf. A194959, A019480, A194982.

Sequence in context: A371247 A361251 A194969 * A057027 A371246 A090894

Adjacent sequences: A194978 A194979 A194980 * A194982 A194983 A194984

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2011

Status

approved