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

0,4

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..1455

Example

If r = i, then g(3) = {3,2r,r+1, r^2}, in which the number of real 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 -> I, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A003237 A191519 A165920 * A190501 A026021 A374690

Adjacent sequences: A274157 A274158 A274159 * A274161 A274162 A274163

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jul 05 2016

Status

approved