A243927 Number of numbers in row n of the array at A243925.

1, 2, 2, 3, 3, 5, 8, 11, 13, 19, 28, 42, 60, 88, 123, 176, 252, 371, 531, 768, 1091, 1581, 2256, 3262, 4685, 6818, 9755, 14167, 20321, 29465, 42275, 61280, 88082, 127736, 183613, 266012, 382840, 554373

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 A243927(n). Conjecture: every rational number occurs exactly once in the array.

Links

Table of n, a(n) for n=1..38.

Example

First 7 rows of the array of rationals:
1/1
-2/1 ... 2/1
-1/1 ... 3/1
-2/3 ... 0/1 ... 4/1
-1/2 ... 1/3 ... 5/1
-6/1 ... -2/5 .. 1/2 ... 4/3 ... 6/1
-5/1 ... -4/1 .. -3/2 .. -1/3 .. 3/5 .. 3/2 .. 7/3 .. 7/1, so that the first 7 terms of A243927 are 1,2,2,3,3,5,8.

Mathematica

z = 20; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -2/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[5] = Delete[g[5], 4]; Table[Length[g[n]], {n, 1, z}]  (* A243927 *)

Crossrefs

Cf. A243925, A243926, A243930.

Sequence in context: A055501 A096010 A241507 * A102330 A103598 A103403

Adjacent sequences: A243924 A243925 A243926 * A243928 A243929 A243930

Keyword

nonn,easy

Author

Clark Kimberling, Jun 15 2014

Status

approved