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

1,2

Comments

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

Links

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

Example

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;

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 *)

Crossrefs

Cf. A194959, A194960, A194962, A194963.

Sequence in context: A265554 A082463 A368432 * A072793 A083047 A191737

Adjacent sequences: A194959 A194960 A194961 * A194963 A194964 A194965

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2011

Status

approved