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

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

Adjacent sequences: A274142 A274143 A274144 * A274146 A274147 A274148

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved