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A274147 Number of integers in n-th generation of tree T(-1/2) defined in Comments.

%I A274147 #14 Jul 04 2016 03:53:23
%S A274147 1,1,1,2,2,4,6,9,13,20,31,48,70,108,165,250,379,575,875,1332,2017,
%T A274147 3066,4661,7076,10751,16328,24801,37684,57229,86931,132062,200588,
%U A274147 304701,462844,703043,1067955,1622207,2464117,3743047,5685655,8636525,13118942,19927624,30270167,45980452,69844296,106093768
%N A274147 Number of integers in n-th generation of tree T(-1/2) defined in Comments.
%C A274147 Let T* be the infinite tree with root 0 generated by these rules:  if p is in T*, then p+1 is in T* and x*p is in T*.  Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc.  Let T(r) be the tree obtained by substituting r for x.
%C A274147 See A274142 for a guide to related sequences.
%H A274147 Kenny Lau, <a href="/A274147/b274147.txt">Table of n, a(n) for n = 0..5503</a>
%e A274147 For r = -1/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.
%p A274147 A274147 := proc(r)
%p A274147     local gs,n,gs2,el,a ;
%p A274147     gs := [2,r] ;
%p A274147     for n from 3 do
%p A274147         gs2 := [] ;
%p A274147         for el in gs do
%p A274147             gs2 := [op(gs2),el+1,r*el] ;
%p A274147         end do:
%p A274147         gs := gs2 ;
%p A274147         a := 0 ;
%p A274147         for el in gs do
%p A274147             if type(el,'integer') then
%p A274147                  a := a+1 :
%p A274147             end if;
%p A274147         end do:
%p A274147         print(n,a) ;
%p A274147     end do:
%p A274147 end proc:
%p A274147 A274147(-1/2) ; # _R. J. Mathar_, Jun 16 2016
%t A274147 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274147 u = Table[t[[k]] /. x -> -1/2, {k, 1, z}]; Table[
%t A274147 Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}] (*A274147*)
%Y A274147 Cf. A274142.
%K A274147 nonn
%O A274147 0,4
%A A274147 _Clark Kimberling_, Jun 11 2016
%E A274147 More terms from _Kenny Lau_, Jul 02 2016