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 A343264 Cardinalities of the sets of fusible numbers obtained at the consecutive steps of their construction as follows. We set S(0) = {0}. S(n+1) is obtained by adding to S(n) the sums (x+y+1)/2 for all x,y from S(n) with the property |x-y| < 1. Then, a(n) is the number of elements in S(n). 2
 1, 2, 4, 9, 21, 50, 119, 281, 656, 1513, 3449, 7777, 17363, 38422, 84355, 183915, 398526, 858901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. Jeff Erickson, Gabriel Nivasch and Junyan Xu, Fusible numbers and Peano Arithmetic, arXiv:2003.14342 [cs.LO], 2020. David A. Corneth, PARI program EXAMPLE a(1) = 2 because S(1) = {0, 1/2}; a(2) = 4 because S(2) = {0, 1/2, 3/4, 1}; a(3) = 9 because S(3) = {0, 1/2, 3/4, 7/8, 1, 9/8, 5/4, 11/8, 3/2}. MAPLE s:= proc(n) option remember; `if`(n=0, {0}, (l-> (m-> {seq([2*x, seq( `if`(abs(x-y) nops(s(n)): seq(a(n), n=0..10); # Alois P. Heinz, Apr 09 2021 MATHEMATICA S[n_]:=S[n]=If[n==0, {0}, S[n-1]\[Union]Map[(#[[1]]+#[[2]]+1)/2&, Select[Tuples[S[n-1], {2}], Abs[#[[1]]-#[[2]]]<1&]]]; Table[Length[S[n]], {n, 0, 12}] PROG (PARI) See Corneth link \\ David A. Corneth, Apr 09 2021 CROSSREFS Cf. A283075. Sequence in context: A322325 A355046 A275864 * A018905 A024537 A171842 Adjacent sequences: A343261 A343262 A343263 * A343265 A343266 A343267 KEYWORD nonn,more AUTHOR Mamuka Jibladze, Apr 09 2021 EXTENSIONS a(13) from Alois P. Heinz, Apr 09 2021 a(14)-a(17) from David A. Corneth, Apr 10 2021 STATUS approved

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Last modified April 23 22:36 EDT 2024. Contains 371917 sequences. (Running on oeis4.)