A243856 - OEIS

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A243856

Number of numbers in row n of the array at A243855.

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

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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];