A194974 Interspersion fractally induced by A194973, a rectangular array, by antidiagonals.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 12, 16, 19, 20, 21, 17, 18, 22, 26, 27, 28, 23, 24, 25, 29, 34, 35, 36, 30, 31, 32, 33, 37, 43, 44, 45, 38, 40, 41, 42, 39, 46, 53, 54, 55, 47, 50, 51, 52, 48, 49, 56, 64, 65, 66, 57, 61, 62, 63, 58, 59, 60, 67, 76, 77

Offset

1,2

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

Links

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

Example

Northwest corner:
1...2...4...7...11
3...5...8...13..19
6...9...14..20..27
10..15..21..28..36
12..17..23..30..38

Mathematica

p[n_] := Floor[(n + 3)/4] + Mod[n - 1, 4]
Table[p[n], {n, 1, 90}]  (* A053737(n+4), n>=0 *)
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]  (* A194973 *)
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}]]  (* A194974 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194975 *)

Crossrefs

Cf. A194959, A194973, A194975.

Sequence in context: A086044 A257456 A257340 * A302839 A130572 A353838

Adjacent sequences: A194971 A194972 A194973 * A194975 A194976 A194977

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2011

Status

approved