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A243856 Number of numbers in row n of the array at A243855. 4
1, 2, 2, 3, 4, 7, 11, 17, 27, 44, 70, 111, 176, 281, 447, 712, 1130, 1797, 2856, 4549, 7233, 11517, 18317, 29163, 46389, 73838, 117503, 187047, 297690, 473909, 754298, 1200808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Decree that (row 1) = (1) and (row 2) = (3,2).  For n >= 4, row n consists of numbers in decreasing order generated as follows:  x+1 for each x in row n-1 together with 3/x for each x in row n-1, and duplicates are rejected as they occur.  Then a(n) = (number of numbers in row n); it appears that this sequence is not linearly recurrent.

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

First 6 rows of the array of rationals:

1/1

4/1 ... 2/1

5/1 ... 3/1

6/1 ... 4/3 ... 4/5

7/1 ... 7/3 ... 9/5 ... 2/3

8/1 ... 10/3 ... 14/5 .. 20/9 .. 12/7 .. 5/3 .. 4/7, so that A243856 begins with 1,2,2,3,4,7.

MATHEMATICA

z = 12; g[1] = {1}; f1[x_] := x + 1; f2[x_] := 4/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]]]

u = Table[Reverse[g[n]], {n, 1, z}]; v = Flatten[u];

Denominator[v] (* A243854 *)

Numerator[v]   (* A243855 *)

Table[Length[g[n]], {n, 1, z}] (* A243856 *)

CROSSREFS

Cf. A243850, A243853.

Sequence in context: A245620 A059348 A110871 * A173433 A053638 A051920

Adjacent sequences:  A243853 A243854 A243855 * A243857 A243858 A243859

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified February 17 17:12 EST 2019. Contains 320222 sequences. (Running on oeis4.)