A274153 Number of integers in n-th generation of tree T(5/2) defined in Comments.

1, 1, 1, 2, 2, 4, 5, 8, 12, 19, 27, 41, 60, 90, 136, 204, 306, 461, 692, 1036, 1557, 2330, 3498, 5247, 7872, 11803, 17715, 26558, 39851, 59781, 89651, 134482, 201736, 302605, 453892, 680800, 1021307, 1531944, 2297678, 3446694, 5170101, 7754719, 11632249, 17448162, 26172247, 39258668, 58886868, 88331299, 132497660

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..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}]

Crossrefs

Cf. A274142.

Sequence in context: A094992 A172128 A274154 * A079501 A093335 A093333

Adjacent sequences: A274150 A274151 A274152 * A274154 A274155 A274156

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jul 02 2016

Status

approved