A195080 Interspersion fractally induced by A008621, a rectangular array, by antidiagonals.

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

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, A194980 is a permutation of the positive integers, with inverse A195081.

Links

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

Example

Northwest corner:
1...3...6...10..15..21..38
2...5...9...14..20..27..35
4...7...11..16..22..29..37
8...13..19..26..34..43..53
12..18..25..33..42..52..63

Mathematica

r = 4; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A008621 *)
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] (* A195079 *)
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}]] (* A195080 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195081 *)

Crossrefs

Cf. A008621, A195079, A195081.

Sequence in context: A195081 A120913 A194922 * A194858 A194857 A194879

Adjacent sequences: A195077 A195078 A195079 * A195081 A195082 A195083

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 08 2011

Status

approved