A274148 Number of integers in n-th generation of tree T(-1/3) defined in Comments.

1, 1, 1, 1, 2, 2, 3, 5, 6, 8, 12, 17, 23, 32, 44, 61, 86, 119, 164, 228, 318, 442, 614, 850, 1181, 1643, 2282, 3167, 4398, 6110, 8489, 11790, 16372, 22737, 31584, 43870, 60930, 84622, 117533, 163248, 226742, 314918, 437389, 607498, 843772, 1171927, 1627699

Offset

0,5

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..7004

Example

For r = -1/3, we have 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 -> -1/3, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A116465 A117356 A017819 * A050044 A308924 A307637

Adjacent sequences: A274145 A274146 A274147 * A274149 A274150 A274151

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved