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

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

Adjacent sequences: A274149 A274150 A274151 * A274153 A274154 A274155

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 02 2016

Status

approved