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A243850 Number of numbers in row n of the array at A243848. 6
1, 1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 74, 117, 184, 291, 455, 719, 1135, 1789, 2821, 4456, 7025, 11097, 17510, 27645, 43668, 68973, 108897, 172051, 271835, 429442, 678573 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Decree that (row 1) = (1), (row 2) = (2), and (row 3) = (3).  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 2/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

2/1

3/1

4/1 ... 2/3

5/1 ... 5/3 ... 1/2

6/1 ... 8/3 ... 3/2 ... 6/5 ... 2/5, so that a begins with 1,1,1,2,3,5.

MATHEMATICA

z = 12; 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]]]

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

Denominator[v] (* A243848 *)

Numerator[v]   (* A243849 *)

Table[Length[g[n]], {n, 1, z}] (* A243850 *)

CROSSREFS

Cf. A243848, A243849, A243853.

Sequence in context: A303668 A060961 A225393 * A179018 A205476 A170805

Adjacent sequences:  A243847 A243848 A243849 * A243851 A243852 A243853

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 12 2014

STATUS

approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)