OFFSET
0,2
LINKS
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)<m, x+y+m, [][]), y=l)][], x=l)})(2^(n-1)))(s(n-1)))
end:
a:= n-> 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
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