A243930 Number of numbers in row n of the array at A243928.

1, 2, 3, 4, 6, 6, 9, 15, 23, 34, 48, 71, 102, 155, 232, 348, 519, 765, 1140, 1691, 2528, 3789, 5634, 8396, 12527, 18709, 27955, 41755, 62410, 93227, 139239, 207939, 310603, 464212, 694207

Offset

1,2

Comments

Decree that (row 1) = (1). For n >=2, row n consists of numbers in increasing order generated as follows: x+1 for each x in row n-1 together with -2/x for each nonzero x in row n-1, where duplicates are deleted as they occur. The number of numbers in row n is A243930(n). Conjecture: every rational number occurs exactly once in the array.

Links

Table of n, a(n) for n=1..35.

Example

First 7 rows of the array of rationals:
1/1
-3/1 .. 2/1
-2/1 .. -3/2 .. 3/1
-1/1 .. -1/2 .. 3/2 ... 4/1
-3/4 .. 0/1 ... 1/2 ... 5/2 .. 5/1 .. 6/1
-6/1 .. -6/5 .. -3/5 .. 1/4 .. 7/2 .. 7/1
-12/1 . -5/1 .. -6/7 .. -3/7 . -1/5 . 2/5 . 5/4 . 9/2 . 8/1, so that the first 7 terms of A243930 are 1,2,3,4,6,6,9.

Mathematica

z = 20; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -3/x; h[1] = g[1];
b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];
h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement[b[n], Intersection[b[n], h[n]]]; g[6] = Delete[g[6], 7];
Table[Length[g[n]], {n, 1, z}]  (* A243930 *)

Crossrefs

Cf. A243927.

Sequence in context: A357476 A034890 A009490 * A064778 A317491 A332295

Adjacent sequences: A243927 A243928 A243929 * A243931 A243932 A243933

Keyword

nonn,easy

Author

Clark Kimberling, Jun 15 2014

Status

approved