A274155 Number of integers in n-th generation of tree T(-5/2) defined in Comments.

1, 1, 1, 2, 2, 4, 6, 8, 12, 19, 28, 42, 63, 95, 145, 212, 321, 479, 723, 1080, 1622, 2436, 3652, 5472, 8212, 12309, 18488, 27718, 41599, 62370, 93578, 140360, 210511, 315787, 473646, 710583, 1065773, 1598933, 2398260, 3597426, 5395845, 8093416, 12140388, 18210490, 27317995

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..48

Example

For r = -5/2, 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 -> -5/2, {k, 1, z}]; Table[
Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}](*A274155*)

Crossrefs

Cf. A274142.

Sequence in context: A123862 A089647 A274152 * A145465 A291055 A266949

Adjacent sequences: A274152 A274153 A274154 * A274156 A274157 A274158

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jun 30 2017

Status

approved