A195074 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.

1, 3, 2, 6, 4, 5, 10, 7, 9, 8, 15, 11, 14, 12, 13, 21, 16, 20, 17, 19, 18, 28, 22, 27, 23, 26, 25, 24, 36, 29, 35, 30, 34, 33, 31, 32, 45, 37, 44, 38, 43, 42, 39, 41, 40, 55, 46, 54, 47, 53, 52, 48, 51, 49, 50, 66, 56, 65, 57, 64, 63, 58, 62, 59, 61, 60, 78, 67, 77

Offset: 1

Author

Clark Kimberling, Sep 08 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, A194974 is a permutation of the positive integers, with inverse A195075.

To see that A195074 differs from A194988, note that the generating sequences A195072 and A194986 differ.

Examples

			Northwest corner:
1...3...6...10..15..21
2...4...7...11..16..22
5...9...14..20..27..35
8...12..17..23..30..38
13..19..26..34..43..53
		

Crossrefs

Cf. A195072, A195074, A195075.

Programs

Mathematica

r = Sqrt[3]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]   (* A195072 *)
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]   (* A195073 *)
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}]]    (* A195074 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]]   (* A195075 *)