A274162 Number of real integers in n-th generation of tree T(3i) defined in Comments.

1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 234, 379, 615, 997, 1617, 2622, 4252, 6895, 11181

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

Table of n, a(n) for n=0..21.

Example

If r = 3i, then g(3) = {3,2r,r+1, r^2}, in which the number of real integers is a(3) = 2.

Mathematica

z = 22; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 3 I, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A069041 A177372 A109609 * A073958 A074317 A077371

Adjacent sequences: A274159 A274160 A274161 * A274163 A274164 A274165

Keyword

nonn,more

Author

Clark Kimberling, Jun 12 2016

Extensions

a(19)-a(21) from Ryan Hitchman, Sep 13 2017

Status

approved