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A243930
Number of numbers in row n of the array at A243928.
5
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.
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 A373700 A317491
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 15 2014
STATUS
approved