A194922 Interspersion fractally induced by A194920, a rectangular array, by antidiagonals.

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

Offset: 1

Author

Clark Kimberling, Sep 08 2011

Keywords

• nonn
• tabl

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, A194922 is a permutation of the positive integers, with inverse A195071.

Examples

			Northwest corner:
   1,  3,  6, 10, 15, 21
   2,  5,  9, 14, 20, 27, 35
   4,  7, 11, 16, 22, 29, 37
   8, 13, 19, 26, 34, 43, 53
  12, 18, 25, 33, 42, 52, 63
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Crossrefs

Cf. A194920, A194921, A195071.

Programs

Mathematica

r = Sqrt[2]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194920 *)
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]  (* A194921 *)
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}]]  (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A195071 *)