%I #9 Jul 04 2016 03:52:59

%S 1,1,1,2,2,4,5,8,12,19,27,41,60,90,136,204,306,461,692,1036,1557,2330,

%T 3498,5247,7872,11803,17715,26558,39851,59781,89651,134482,201736,

%U 302605,453892,680800,1021307,1531944,2297678,3446694,5170101,7754719,11632249,17448162,26172247,39258668,58886868,88331299,132497660

%N Number of integers in n-th generation of tree T(5/2) defined in Comments.

%C 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 See A274142 for a guide to related sequences.

%e For r = 5/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.

%t z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];

%t u = Table[t[[k]] /. x -> 5/2, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

%Y Cf. A274142.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Jun 12 2016

%E More terms from _Kenny Lau_, Jul 02 2016