A194051 Natural interspersion of A194050, a rectangular array, by antidiagonals.

1, 2, 3, 5, 6, 4, 9, 10, 7, 8, 16, 17, 11, 12, 13, 27, 28, 18, 19, 20, 14, 45, 46, 29, 30, 31, 21, 15, 74, 75, 47, 48, 49, 32, 22, 23, 121, 122, 76, 77, 78, 50, 33, 34, 24, 197, 198, 123, 124, 125, 79, 51, 52, 35, 25, 320, 321, 199, 200, 201, 126, 80, 81, 53

Offset

1,2

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194051 is a permutation of the positive integers; its inverse is A194052.

Links

Table of n, a(n) for n=1..64.

Example

Northwest corner:
1...2...5...9...16
3...6...10..17..28
4...7...11..18..29
8...12..19..30..48
13..20..31..49..78

Mathematica

z = 50;
c[k_] := LucasL[k + 1] - 2;
c = Table[c[k], {k, 1, z}]  (* A014739 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 600}]  (* A194050 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194051 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194052 *)

Crossrefs

Cf. A194029, A014739, A194050, A104052.

Sequence in context: A054077 A194872 A194900 * A195610 A342038 A082654

Adjacent sequences: A194048 A194049 A194050 * A194052 A194053 A194054

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 13 2011

Status

approved