A274146 Number of integers in n-th generation of tree T(3/4) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 12, 16, 18, 24, 28, 35, 41, 53, 63, 79, 95, 119, 145, 181, 221, 275, 339, 421, 519, 645, 798, 991, 1228, 1525, 1890, 2350, 2915, 3622, 4495, 5588, 6939, 8626, 10712, 13315, 16545, 20567, 25556, 31766, 39483, 49081, 61007, 75836, 94270, 117194, 145688

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..10561

Example

For r = 3/4, we have g(3) = {3,2r,r+1, r^2}, in which only 3 is an integer, so that a(3) = 1.

Mathematica

z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> 3/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A069910 A026797 A008484 * A027189 A140829 A346523

Adjacent sequences: A274143 A274144 A274145 * A274147 A274148 A274149

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved