A274144 Number of integers in n-th generation of tree T(1/4) defined in Comments.

1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 5, 8, 8, 9, 12, 16, 17, 21, 27, 32, 37, 47, 57, 67, 82, 102, 121, 145, 180, 219, 260, 317, 391, 470, 564, 691, 843, 1012, 1225, 1500, 1816, 2188, 2663, 3245, 3918, 4744, 5778, 7010, 8473, 10291, 12511, 15148

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..11916

Example

For r = 1/4, 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 -> 1/4, {k, 1, z}];
Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A029079 A035398 A104409 * A214628 A355806 A032576

Adjacent sequences: A274141 A274142 A274143 * A274145 A274146 A274147

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2016

Extensions

More terms from Kenny Lau, Jul 01 2016

Status

approved