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%I #4 Jun 19 2014 11:18:37
%S 1,2,2,3,3,5,8,11,13,19,28,42,60,88,123,176,252,371,531,768,1091,1581,
%T 2256,3262,4685,6818,9755,14167,20321,29465,42275,61280,88082,127736,
%U 183613,266012,382840,554373
%N Number of numbers in row n of the array at A243925.
%C 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.
%e First 7 rows of the array of rationals:
%e 1/1
%e -2/1 ... 2/1
%e -1/1 ... 3/1
%e -2/3 ... 0/1 ... 4/1
%e -1/2 ... 1/3 ... 5/1
%e -6/1 ... -2/5 .. 1/2 ... 4/3 ... 6/1
%e -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.
%t z = 20; g[1] = {1}; f1[x_] := x + 1; f2[x_] := -2/x; h[1] = g[1];
%t b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]];
%t h[n_] := h[n] = Union[h[n - 1], g[n - 1]];
%t 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 *)
%Y Cf. A243925, A243926, A243930.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 15 2014
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