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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
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
Cf. A283075.
Sequence in context: A322325 A355046 A275864 * A018905 A024537 A171842
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.)