A274145 - OEIS

A274145

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

1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 9, 11, 14, 19, 25, 32, 43, 56, 73, 97, 128, 167, 222, 292, 384, 507, 670, 882, 1165, 1539, 2030, 2680, 3541, 4675, 6173, 8155, 10772, 14227, 18798, 24834, 32808, 43350, 57279, 75681, 100006, 132152, 174627, 230766, 304963, 403012, 532600, 703874, 930227, 1229386

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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..8248

EXAMPLE

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

MATHEMATICA

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

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

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

CROSSREFS

Cf. A274142.

Sequence in context: A308283 A336133 A238625 * A036072 A045475 A316078