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

0,4

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.

Links

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

Example

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

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*)

Crossrefs

Cf. A274142.

Sequence in context: A306730 A209603 A192684 * A226496 A047084 A058518

Adjacent sequences: A274144 A274145 A274146 * A274148 A274149 A274150

Keyword

nonn

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 02 2016

Status

approved