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A274146
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Number of integers in n-th generation of tree T(3/4) defined in Comments.
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2
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1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 12, 16, 18, 24, 28, 35, 41, 53, 63, 79, 95, 119, 145, 181, 221, 275, 339, 421, 519, 645, 798, 991, 1228, 1525, 1890, 2350, 2915, 3622, 4495, 5588, 6939, 8626, 10712, 13315, 16545, 20567, 25556, 31766, 39483, 49081, 61007, 75836, 94270, 117194, 145688
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OFFSET
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0,6
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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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For r = 3/4, we have g(3) = {3,2r,r+1, r^2}, in which only 3 is an integer, so that a(3) = 1.
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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 -> 3/4, {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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