%I A122554
%S A122554 1,3,6,10,15,23,35,54,84,132,209,333,533,856,1378,2222,3587,5795,9367,
%T A122554 15146,24496,39624,64101,103705,167785,271468,439230,710674,1149879,
%U A122554 1860527,3010379,4870878,7881228
%N A122554 Let S(1)={1} and, for n>1 let S(n) be the smallest set containing x, 
               2x and x+2 for each element x in S(n-1). a(n) is the number of elements 
               in S(n).
%C A122554 If the set mapping has x -> x,2x,x^2 is used instead of x -> x,x+2,2x, 
               the corresponding sequence consists of the Fibonacci numbers 1,2,
               3,5,8,...
%C A122554 Apparently a(n)= 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4) for n>6, equivalent 
               to a(n)=A000032(n)+n-1 for n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.n), 
               Nov 18 2009]
%e A122554 Under the indicated set mapping we have {1} -> {1,2,3} -> {1,2,3,4,5,
               6} -> {1,2,3,4,5,6,7,8,10,12},..., so a(2)=3, a(3)=6, a(4)=10, etc.
%t A122554 Do[ Print@ Length@ Nest[ Union@ Flatten[ # /. a_Integer -> {a, 2a, a 
               + 2}] &, {1}, n], {n, 0, 32}] - Robert G. Wilson v Sep 27 2006
%Y A122554 Sequence in context: A143963 A139714 A063542 this_sequence A111734 A117457 
               A024674
%Y A122554 Adjacent sequences: A122551 A122552 A122553 this_sequence A122555 A122556 
               A122557
%K A122554 nonn,new
%O A122554 1,2
%A A122554 John W. Layman (layman(AT)math.vt.edu), Sep 20 2006
%E A122554 a(17) - a(33) from Robert G. Wilson v Sep 27 2006