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

Author

Clark Kimberling, Jun 15 2014

Keywords

• nonn
• easy

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.

Examples

			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.
		

Crossrefs

Cf. A243927.

Programs

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 *)