A194984 Interspersion fractally induced by A194964, 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, 24, 25, 36, 29, 35, 30, 34, 31, 33, 32, 45, 37, 44, 38, 43, 39, 42, 40, 41, 55, 46, 54, 47, 53, 48, 52, 49, 51, 50, 66, 56, 65, 57, 64, 58, 63, 59, 62, 61, 60, 78, 67, 77

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, A194984 is a permutation of the positive integers, with inverse A194985.

Examples

			Northwest corner:
1...3...6...10..15..21..28
2...4...7...11..16..22..29
5...9...14..20..27..35..44
8...12..17..23..30..38..47
13..19..26..34..43..53..64
		

Crossrefs

Cf. A194959, A194964, A194983, A194985.

Programs

Mathematica

r = Sqrt[5]; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194964 *)
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] (* A194983 *)
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}]]  (* A194984 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194985 *)