A194050 -id:A194050 - cp's OEIS frontend

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

Clark Kimberling, Aug 13 2011

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.

			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

Cf. A194029, A014739, A194050, A104052.

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 *)

cp's OEIS Frontend

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

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