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A274143 Number of integers in n-th generation of tree T(1/3) defined in Comments. 2
1, 1, 1, 1, 2, 2, 2, 4, 4, 5, 8, 9, 12, 16, 20, 26, 34, 44, 57, 74, 97, 125, 162, 212, 272, 356, 462, 597, 780, 1010, 1311, 1706, 2210, 2873, 3732, 4841, 6294, 8168, 10608, 13781, 17886, 23237, 30172, 39177, 50891, 66072, 85813, 111446, 144706, 187947, 244059, 316937, 411618, 534503, 694153, 901461 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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..8805

EXAMPLE

For r = 1/3, we have g(3) = {3,2r,r+1, r^2}, in which only 3 is an integer, so that a(3) = 1.

MAPLE

A274143 := 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:

A274143(1/3) ; # R. J. Mathar, Jun 17 2016

MATHEMATICA

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

u = Table[t[[k]] /. x -> 1/3, {k, 1, z}];

Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

CROSSREFS

Cf. A274142.

Sequence in context: A272397 A239729 A005859 * A166271 A237520 A268241

Adjacent sequences:  A274140 A274141 A274142 * A274144 A274145 A274146

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 11 2016

EXTENSIONS

More terms from Kenny Lau, Jul 04 2016

STATUS

approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)