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

Author

Clark Kimberling, Sep 07 2011

Keywords

• nonn
• tabl

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.

Examples

			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
		

Crossrefs

Cf. A194959, A019480, A194982.

Programs

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 *)