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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.

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`%I #11 Jun 18 2017 19:44:07
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`%S 1,3,7,21,83,484,4084,49479
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`%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.
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`%e The sets of numbers obtainable at the n-th step are:
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`%e S(0) = { 1 },
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`%e S(1) = { 0, 1, 2 },
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`%e S(2) = { -1, 0, 1/2, 1, 2, 3, 4 },
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`%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 }.
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`%Y Cf. A214872, A288759, A288850.
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`%Y A216999 provides the corresponding results if division is not used.
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`%K nonn,hard,more
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`%O 0,2
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`%A _Hugo Pfoertner_, Jun 18 2017
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`%E a(7) from _Alois P. Heinz_, Jun 18 2017
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