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 A274142 Number of integers in n-th generation of tree T(1/2) defined in Comments. 30
 1, 1, 1, 2, 2, 4, 5, 8, 11, 17, 25, 37, 54, 81, 119, 177, 261, 388, 574, 851, 1260, 1868, 2767, 4101, 6077, 9006, 13347, 19781, 29315, 43448, 64392, 95436, 141444, 209636, 310705, 460501, 682519, 1011581, 1499295, 2222155, 3293534, 4881472, 7235018, 10723311, 15893460, 23556367, 34913897, 51747400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. Guide to related sequences: r           sequence 1/2         A274142 1/3         A274143 1/4         A274144 2/3         A274145 3/4         A274146 -1/2        A274147 -1/3        A274148 -1/4        A274149 -2/3        A274150 -3/4        A274151 3/2         A274152 5/2         A274153 -3/2        A274154 -5/2        A274155 2^(1/2)     A000045 (Fibonacci numbers) 2^(1/3)     A000930 2^(1/4)     A003269 2^(-1/2)    A274156 3^(-1/2)    A274157 2^(-1/3)    A274158 3^(-1/3)    A274159 i           A274160 2i          A206743 3i          A274162 4i          A274163 i/2         A274149 i/3         A274165 i+1         A274166 i-1         A274167 (-1+3i)/2   A274168 LINKS Kenny Lau, Table of n, a(n) for n = 0..5847 EXAMPLE If r = 1/2, then g(3) = {3,2r,r+1, r^2}, in which the integers are 3 and 1, so that a(3) = 2. MATHEMATICA z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]]; u = Table[t[[k]] /. x -> 1/2, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}] (* second program: *) T = {0}; T[n_] := T[n] = Complement[Join[T[n-1]+1, x*T[n-1]], T[n-1]]; Reap[For[n = 0, n <= 25, n++, cnt = Count[T[n] /. x -> 1/2, _Integer]; Print[n, " ", cnt]; Sow[cnt]]][[2, 1]] (* Jean-François Alcover, Jun 14 2016 *) CROSSREFS Cf. A274143-A274160, A274162, A274163, A274165-A274168. Sequence in context: A238478 A013979 A107458 * A006206 A060280 A095719 Adjacent sequences:  A274139 A274140 A274141 * A274143 A274144 A274145 KEYWORD nonn AUTHOR Clark Kimberling, Jun 11 2016 EXTENSIONS More terms from Jean-François Alcover, Jun 14 2016 More terms from Kenny Lau, Jul 04 2016 STATUS approved

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Last modified August 13 02:05 EDT 2020. Contains 336441 sequences. (Running on oeis4.)