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A195114
Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.
3
1, 3, 2, 6, 4, 5, 10, 7, 8, 9, 15, 12, 13, 14, 11, 21, 18, 19, 20, 16, 17, 28, 25, 26, 27, 22, 23, 24, 36, 33, 34, 35, 29, 30, 31, 32, 45, 42, 43, 44, 38, 39, 40, 41, 37, 55, 52, 53, 54, 48, 49, 50, 51, 46, 47, 66, 63, 64, 65, 59, 60, 61, 62, 56, 57, 58, 78, 75, 76
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, A194114 is a permutation of the positive integers, with inverse A195115.
EXAMPLE
Northwest corner:
1...3...6...10..15..21..28
2...4...7...12..18..25..33
5...8...13..19..26..34..43
9...14..20..27..35..44..54
11..16..22..29..38..48..59
MATHEMATICA
j[n_] := Table[k, {k, 1, n}];
t[1] = j[1]; t[2] = j[1];
t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1, 1, 2 repl by 1 *)
t[12]
p[n_] := t[20][[n]]
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] (* A195113 *)
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}]] (* A195114 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195115 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 09 2011
STATUS
approved