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A274159 Number of integers in n-th generation of tree T(3^(-1/3)) defined in Comments. 2
1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 12, 16, 18, 23, 28, 33, 41, 49, 61, 72, 89, 107, 130, 159, 191, 234, 283, 345, 418, 507, 617, 747, 910, 1103, 1340, 1629, 1976, 2402, 2914, 3542, 4300, 5223, 6344, 7701, 9359, 11361, 13801, 16761, 20353, 24725, 30021, 36468, 44285, 53788, 65328 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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..11841

EXAMPLE

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

MAPLE

A274159 := proc(r)

local gs, n, gs2, el, a ;

gs := [1] ;

for n from 2 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:

A274159(1/root[3](3)) ; # R. J. Mathar, Jun 20 2016

MATHEMATICA

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

u = Table[t[[k]] /. x -> 3^(-1/3), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

CROSSREFS

Cf. A274142.

Sequence in context: A238210 A120170 A136421 * A239905 A016085 A018122

Adjacent sequences: A274156 A274157 A274158 * A274160 A274161 A274162

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 12 2016

EXTENSIONS

a(15)-a(18) from R. J. Mathar, Jun 20 2016

More terms from Kenny Lau, Jul 04 2016

STATUS

approved

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Last modified January 27 06:42 EST 2023. Contains 359837 sequences. (Running on oeis4.)