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

1,2

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, 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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A195072, A195074, A195075.

Sequence in context: A059399 A194984 A194988 * A194918 A194915 A195077

Adjacent sequences: A195071 A195072 A195073 * A195075 A195076 A195077

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 08 2011

Status

approved