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

1,2

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A194959, A037915, A195097, A195099.

Sequence in context: A065673 A077168 A195099 * A102452 A000401 A023807

Adjacent sequences: A195095 A195096 A195097 * A195099 A195100 A195101

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 08 2011

Status

approved