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A274160
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Number of real integers in n-th generation of tree T(i) defined in Comments.
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7
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1, 1, 1, 2, 3, 6, 10, 19, 33, 62, 112, 212, 394, 751, 1419, 2719, 5193, 10002, 19254, 37258, 72132, 140108, 272368, 530646, 1034798, 2021127, 3951147, 7733421, 15148711, 29702087, 58279135, 114438213, 224856997, 442099674, 869717486, 1711885120, 3371215170, 6642102554, 13092289634, 25817134600
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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EXAMPLE
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If r = i, then g(3) = {3,2r,r+1, r^2}, in which the number of real integers is a(3) = 2.
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MATHEMATICA
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z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
u = Table[t[[k]] /. x -> I, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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