

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 xy < 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
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OFFSET

0,2


LINKS



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(xy)<m, x+y+m, [][]), y=l)][], x=l)})(2^(n1)))(s(n1)))
end:
a:= n> nops(s(n)):


MATHEMATICA

S[n_]:=S[n]=If[n==0, {0}, S[n1]\[Union]Map[(#[[1]]+#[[2]]+1)/2&, Select[Tuples[S[n1], {2}], Abs[#[[1]]#[[2]]]<1&]]]; Table[Length[S[n]], {n, 0, 12}]


PROG



CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



