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Number of distinct rational numbers that can be obtained in n steps by a straight-line program (SLP) starting at 1 using addition, subtraction, multiplication and division.
3

%I #11 Jun 18 2017 19:44:07

%S 1,3,7,21,83,484,4084,49479

%N Number of distinct rational numbers that can be obtained in n steps by a straight-line program (SLP) starting at 1 using addition, subtraction, multiplication and division.

%e The sets of numbers obtainable at the n-th step are:

%e S(0) = { 1 },

%e S(1) = { 0, 1, 2 },

%e S(2) = { -1, 0, 1/2, 1, 2, 3, 4 },

%e S(3) = { -3, -2, -3/2, -1, -1/2, 0, 1/4, 1/3, 1/2, 2/3, 1, 3/2, 2, 5/2, 3, 4, 5, 6, 8, 9, 16 }.

%Y Cf. A214872, A288759, A288850.

%Y A216999 provides the corresponding results if division is not used.

%K nonn,hard,more

%O 0,2

%A _Hugo Pfoertner_, Jun 18 2017

%E a(7) from _Alois P. Heinz_, Jun 18 2017