

A274168


Number of real integers in nth generation of tree T(r) defined in Comments, where r^2 = r  1 (i.e., r = (1 + sqrt(3))/2).


1



1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 9, 13, 18, 25, 33, 43
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OFFSET

0,7


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 nth 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

Table of n, a(n) for n=0..18.


EXAMPLE

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


CROSSREFS

Cf. A274142.
Sequence in context: A027189 A140829 A184324 * A116575 A244800 A275972
Adjacent sequences: A274165 A274166 A274167 * A274169 A274170 A274171


KEYWORD

nonn,more


AUTHOR

Clark Kimberling, Jun 13 2016


STATUS

approved



