A274152 - OEIS

A274152

Number of integers in n-th generation of tree T(3/2) defined in Comments.

1, 1, 1, 2, 2, 4, 6, 8, 12, 18, 28, 42, 62, 96, 142, 210, 316, 474, 712, 1070, 1606, 2410, 3608, 5412, 8124, 12184, 18268, 27404, 41114, 61662, 92484, 138702, 208020, 311988, 467928, 701866, 1052812, 1579204, 2368764, 3553048, 5329306, 7993478, 11989564, 17983626, 26974744, 40461664, 60692460

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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..73

EXAMPLE

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

MATHEMATICA

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

u = Table[t[[k]] /. x -> 3/2, {k, 1, z}];

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

CROSSREFS

Cf. A274142.

Sequence in context: A091915 A123862 A089647 * A274155 A145465 A291055