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A195098
Interspersion fractally induced by (1+[3n/4]), where [ ] = floor; a rectangular array, by antidiagonals.
3
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 08 2011
STATUS
approved