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 A274144 Number of integers in n-th generation of tree T(1/4) defined in Comments. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 A032576 A276420 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

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Last modified August 7 10:34 EDT 2020. Contains 336275 sequences. (Running on oeis4.)