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A274155 Number of integers in n-th generation of tree T(-5/2) defined in Comments.

%I A274155 #15 Jul 01 2017 03:00:50
%S A274155 1,1,1,2,2,4,6,8,12,19,28,42,63,95,145,212,321,479,723,1080,1622,2436,
%T A274155 3652,5472,8212,12309,18488,27718,41599,62370,93578,140360,210511,
%U A274155 315787,473646,710583,1065773,1598933,2398260,3597426,5395845,8093416,12140388,18210490,27317995
%N A274155 Number of integers in n-th generation of tree T(-5/2) defined in Comments.
%C A274155 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.
%C A274155 See A274142 for a guide to related sequences.
%H A274155 Kenny Lau, <a href="/A274155/b274155.txt">Table of n, a(n) for n = 0..48</a>
%e A274155 For r = -5/2, we have g(3) = {3,2r,r+1, r^2}, in which the number of integers is a(3) = 2.
%t A274155 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274155 u = Table[t[[k]] /. x -> -5/2, {k, 1, z}]; Table[
%t A274155 Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}](*A274155*)
%Y A274155 Cf. A274142.
%K A274155 nonn,easy
%O A274155 0,4
%A A274155 _Clark Kimberling_, Jun 12 2016
%E A274155 More terms from _Kenny Lau_, Jun 30 2017