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

1, 1, 1, 2, 2, 4, 6, 9, 13, 20, 31, 48, 70, 108, 165, 250, 379, 575, 875, 1332, 2017, 3066, 4661, 7076, 10751, 16328, 24801, 37684, 57229, 86931, 132062, 200588, 304701, 462844, 703043, 1067955, 1622207, 2464117, 3743047, 5685655, 8636525, 13118942, 19927624, 30270167, 45980452, 69844296, 106093768

Offset: 0

Author

Clark Kimberling, Jun 11 2016

Keywords

• nonn

Comments

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.

See A274142 for a guide to related sequences.

Examples

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

Links

• Kenny Lau, Table of n, a(n) for n = 0..5503

Crossrefs

Cf. A274142.

Programs

Maple

A274147 := proc(r)
    local gs,n,gs2,el,a ;
    gs := [2,r] ;
    for n from 3 do
        gs2 := [] ;
        for el in gs do
            gs2 := [op(gs2),el+1,r*el] ;
        end do:
        gs := gs2 ;
        a := 0 ;
        for el in gs do
            if type(el,'integer') then
                 a := a+1 :
            end if;
        end do:
        print(n,a) ;
    end do:
end proc:
A274147(-1/2) ; # R. J. Mathar, Jun 16 2016

Mathematica

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> -1/2, {k, 1, z}]; Table[
Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}] (*A274147*)

Extensions

More terms from Kenny Lau, Jul 02 2016