A195098 Interspersion fractally induced by (1+[3n/4]), where [ ] = floor; a rectangular array, by antidiagonals.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14, 16, 17, 18, 21, 19, 20, 22, 23, 24, 28, 25, 26, 27, 29, 30, 31, 36, 32, 33, 34, 35, 37, 38, 39, 45, 40, 41, 42, 44, 43, 46, 47, 48, 55, 49, 50, 51, 54, 52, 53, 56, 57, 58, 66, 59, 60, 61, 65, 62, 63, 64, 67, 68, 69

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, A194998 is a permutation of the positive integers, with inverse A195099.

Examples

			Northwest corner:
1...2...4...7...11..16..22
3...5...8...12..17..23..30
6...9...13..18..24..31..39
10..15..21..28..36..45..55
14..19..25..32..40..49..59
		

Crossrefs

Cf. A194959, A037915, A195097, A195099.

Programs

Mathematica

r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)
Table[p[n], {n, 1, 90}]
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]    (* A195097 *)
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}]](* A195098 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]](* A195099 *)