A274158 Number of integers in n-th generation of tree T(2^(-1/3)) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 9, 13, 17, 22, 27, 36, 47, 61, 77, 101, 132, 171, 219, 285, 370, 480, 619, 803, 1042, 1351, 1747, 2264, 2936, 3805, 4927, 6385, 8276, 10725, 13894, 18004, 23333, 30238, 39179, 50770, 65794, 85261, 110483, 143171, 185534, 240432, 311566, 403749, 523216, 678031

Offset

0,6

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..8877

Example

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

Mathematica

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 2^(-1/3), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A002723 A035937 A240201 * A020999 A309712 A079955

Adjacent sequences: A274155 A274156 A274157 * A274159 A274160 A274161

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jul 04 2016

Status

approved