A274154 Number of integers in n-th generation of tree T(-3/2) defined in Comments.

1, 1, 1, 2, 2, 4, 5, 8, 12, 18, 27, 41, 60, 92, 134, 206, 305, 463, 694, 1041, 1561, 2344, 3506, 5279, 7903, 11877, 17823, 26689, 40100, 60041, 90217, 135312, 202940, 304555, 456295, 685209, 1027291, 1541669, 2312510, 3466919, 5203662, 7801283, 11707295, 17559032, 26334864

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..72

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: A078465 A094992 A172128 * A274153 A079501 A093335

Adjacent sequences: A274151 A274152 A274153 * A274155 A274156 A274157

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jun 30 2017

Status

approved