A194048 Natural interspersion of A000330, a rectangular array, by antidiagonals.

1, 5, 2, 14, 6, 3, 30, 15, 7, 4, 55, 31, 16, 8, 9, 91, 56, 32, 17, 18, 10, 140, 92, 57, 33, 34, 19, 11, 204, 141, 93, 58, 59, 35, 20, 12, 285, 205, 142, 94, 95, 60, 36, 21, 13, 385, 286, 206, 143, 144, 96, 61, 37, 22, 23

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, A194048 is a permutation of the positive integers; its inverse is A194049.

Links

Table of n, a(n) for n=1..55.

Example

Northwest corner:
1...5...14...30...55
2...6...15...31...56
3...7...16...32...57
4...8...17...33...58
9...18..34...59...95

Mathematica

Remove["Global`*"];
z = 30;
c[k_] := k (k + 1) (2 k + 1)/6;
c = Table[c[k], {k, 1, z}]  (* A000330 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 500}]  (* fractal sequence [A064866] *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 10}, {k, 1, n}]]  (* A194048 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194049 *)

Crossrefs

Cf. A194029, A194049.

Sequence in context: A277710 A286148 A369369 * A158868 A104634 A194008

Adjacent sequences: A194045 A194046 A194047 * A194049 A194050 A194051

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 13 2011

Status

approved