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 A048249 Number of distinct values produced from sums and products of n unity arguments. 14
 1, 2, 3, 4, 6, 9, 11, 17, 23, 30, 44, 60, 80, 114, 156, 212, 296, 404, 556, 770, 1065, 1463, 2032, 2795, 3889, 5364, 7422, 10300, 14229, 19722, 27391, 37892, 52599, 73075, 101301, 140588, 195405, 271024, 376608, 523518, 726812, 1010576, 1405013, 1952498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Values listed calculated by exhaustive search algorithm. For n+1 operands (n operations) there are (2n)!/((n!)((n+1)!)) possible postfix forms over a single operator. For each such form, there are 2^n ways to assign 2 operators (here, sum and product). Calculate results and eliminate duplicates. Number of distinct positive integers that can be obtained by iteratively adding or multiplying together parts of an integer partition until only one part remains, starting with 1^n. - Gus Wiseman, Sep 29 2018 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..75 FORMULA Equals partial sum of "number of numbers of complexity n" (A005421). - Jonathan Vos Post, Apr 07 2006 EXAMPLE a(3)=3 since (in postfix): 111** = 11*1* = 1, 111*+ = 11*1+ = 111+* = 11+1* = 2 and 111++ = 11+1+ = 3. Note that at n=7, the 11 possible values produced are the set {1,2,3,4,5,6,7,8,9,10,12}. This is the first n for which there are "skipped" values in the set. MAPLE b:= proc(n) option remember; `if`(n=1, {1}, {seq(seq(seq(      [f+g, f*g][], g=b(n-i)), f=b(i)), i=1..iquo(n, 2))})     end: a:= n-> nops(b(n)): seq(a(n), n=1..35);  # Alois P. Heinz, May 05 2019 MATHEMATICA ReplaceListRepeated[forms_, rerules_]:=Union[Flatten[FixedPointList[Function[pre, Union[Flatten[ReplaceList[#, rerules]&/@pre, 1]]], forms], 1]]; Table[Length[Select[ReplaceListRepeated[{Array[1&, n]}, {{foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x+y]], {foe___, x_, mie___, y_, afe___}:>Sort[Append[{foe, mie, afe}, x*y]]}], Length[#]==1&]], {n, 10}] (* Gus Wiseman, Sep 29 2018 *) CROSSREFS Cf. A000792, A005520, A066739, A070960, A201163, A319850, A318949, A319855, A319856, A319909, A319910, A319911. Sequence in context: A007210 A198394 A035947 * A288734 A332034 A332035 Adjacent sequences:  A048246 A048247 A048248 * A048250 A048251 A048252 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from David W. Wilson, Oct 10 2001 a(43)-a(44) from Alois P. Heinz, May 05 2019 STATUS approved

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Last modified June 2 13:58 EDT 2020. Contains 334780 sequences. (Running on oeis4.)