A274165 Number of real integers in n-th generation of tree T(i/3) defined in Comments.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 17, 21, 26, 32, 39, 47, 57, 67, 79, 93, 110, 131, 157, 189, 228, 276, 332, 399, 478, 571, 681, 812, 969, 1158, 1387, 1662, 1994, 2393, 2871, 3442, 4123, 4935, 5904, 7063, 8449, 10111

Offset

0,12

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.

a(n) = A017885(n+7) for 2 <= n < 85, but a(85) = 1314173 differs from A017885(92) = 1314172. - Georg Fischer, Oct 30 2018

Links

Kenny Lau, Table of n, a(n) for n = 0..4727

Example

If r = i/3, then g(3) = {3,2r,r+1, r^2}, in which the number of real 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 -> I/3, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]

Crossrefs

Cf. A274142.

Sequence in context: A017896 A118868 A017885 * A011874 A000115 A367253

Adjacent sequences: A274162 A274163 A274164 * A274166 A274167 A274168

Keyword

nonn

Author

Clark Kimberling, Jun 12 2016

Extensions

More terms from Kenny Lau, Jun 30 2017

Status

approved