login
A195083
Interspersion fractally induced by (1+[2n/3]), where [ ] = floor; a rectangular array, by antidiagonals.
3
1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 15, 13, 14, 16, 17, 21, 18, 19, 20, 22, 23, 28, 24, 25, 27, 26, 29, 30, 36, 31, 32, 35, 33, 34, 37, 38, 45, 39, 40, 44, 41, 42, 43, 46, 47, 55, 48, 49, 54, 50, 51, 53, 52, 56, 57, 66, 58, 59, 65, 60, 61, 64, 62, 63, 67, 68, 78
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, A194983 is a permutation of the positive integers, with inverse A195096.
EXAMPLE
Northwest corner:
1...2...4...7...11..16
3...5...8...12..17..23
6...10..15..21..28..36
9...13..18..24..31..39
14..19..25..32..40..49
MATHEMATICA
r = 2/3; p[n_] := 1 + Floor[n*r]
Table[p[n], {n, 1, 90}] (* ess A004396 *)
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] (* A195082 *)
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}]] (* A195083 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195096 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 08 2011
STATUS
approved