A194962 Interspersion fractally induced by A194960.

1, 2, 3, 4, 5, 6, 7, 9, 10, 8, 11, 14, 15, 12, 13, 16, 20, 21, 17, 18, 19, 22, 27, 28, 23, 25, 26, 24, 29, 35, 36, 30, 33, 34, 31, 32, 37, 44, 45, 38, 42, 43, 39, 40, 41, 46, 54, 55, 47, 52, 53, 48, 50, 51, 49, 56, 65, 66, 57, 63, 64, 58, 61, 62, 59, 60, 67, 77, 78, 68, 75, 76, 69, 73, 74, 70, 71, 72

Offset: 1

Author

Clark Kimberling, Sep 07 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			Northwest corner:
   1...2...4...7..11..16..22
   3...5...9..14..20..27..35
   6..10..15..21..28..36..45
   8..12..17..23..30..38..47
  18..13..25..33..42..52..63
Antidiagonals of the array:
   1;
   2,  3;
   4,  5,  6;
   7,  9, 10,  8;
  11, 14, 15, 12, 13;
  16, 20, 21, 17, 18, 19;
  22, 27, 28, 23, 25, 26, 24;
  29, 35, 36, 30, 33, 34, 31, 32;
  37, 44, 45, 38, 42, 43, 39, 40, 41;
		

Links

• G. C. Greubel, Antidiagonals n = 0..50, flattened

Crossrefs

Cf. A194959, A194960, A194962, A194963.

Programs

Mathematica

p[n_] := Floor[(n + 2)/3] + Mod[n - 1, 3]
Table[p[n], {n, 1, 90}]  (* A194960 *)
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]  (* A194961 *)
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}]]  (* A194962 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]]  (* A194963 *)