A274157 Number of integers in n-th generation of tree T(3^(-1/2)) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 9, 11, 14, 16, 22, 26, 33, 40, 53, 62, 82, 97, 127, 151, 198, 234, 309, 366, 480, 570, 749, 887, 1165, 1382, 1815, 2153, 2827, 3353, 4405, 5224, 6859, 8137, 10687, 12675, 16646, 19746, 25932, 30761, 40395, 47917, 62929, 74647, 98027, 116285, 152711, 181150

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..10382

Example

If r = 3^(-1/2), 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 -> 3^(-1/2), {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A130084 A017981 A274759 * A005863 A015740 A015750

Adjacent sequences: A274154 A274155 A274156 * A274158 A274159 A274160

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jul 04 2016

Status

approved