A274160 Number of real integers in n-th generation of tree T(i) defined in Comments.

1, 1, 1, 2, 3, 6, 10, 19, 33, 62, 112, 212, 394, 751, 1419, 2719, 5193, 10002, 19254, 37258, 72132, 140108, 272368, 530646, 1034798, 2021127, 3951147, 7733421, 15148711, 29702087, 58279135, 114438213, 224856997, 442099674, 869717486, 1711885120, 3371215170, 6642102554, 13092289634, 25817134600

Offset: 0

Author

Clark Kimberling, Jun 12 2016

Keywords

• nonn
• easy

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.

Examples

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

Links

• Kenny Lau, Table of n, a(n) for n = 0..1455

Crossrefs

Cf. A274142.

Programs

Mathematica

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> I, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Extensions

More terms from Kenny Lau, Jul 05 2016