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A255810
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Infinite tree (flattened) generated as follows: generation g(1) = (1); thereafter, putting h = 3^n, each (1,x(2),...,x(h)) in generation g(n) has 1st, 2nd, and 3rd offspring, namely (1,x(2),...,x(h),x(h)+1), (1,x(2),...,x(h),x(h)+2) and (1,x(2),...,h(h),x(h)+3).
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2
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1, 1, 2, 1, 3, 1, 4, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 3, 4, 1, 3, 5, 1, 3, 6, 1, 4, 5, 1, 4, 6, 1, 4, 7, 1, 2, 3, 4, 1, 2, 3, 5, 1, 2, 3, 6, 1, 2, 4, 5, 1, 2, 4, 6, 1, 2, 4, 7, 1, 2, 5, 6, 1, 2, 5, 7, 1, 2, 5, 8, 1, 3, 4, 5, 1, 3, 4, 6, 1, 3, 4, 7, 1, 3, 5, 6
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OFFSET
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1,3
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COMMENTS
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Generation n consists of 3^(n-1) increasing n-tuples that have maximal gapsize 3.
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LINKS
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EXAMPLE
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generation g(1) = (1);
g(2) = (1,2), (1,3), (1,4);
g(3) = (1,2,3), (1,2,4), (1,2,5), (1,3,4), (1,3,5), (1,3,6), (1,4,5), (1,4,6), (1,4,7).
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MATHEMATICA
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width = 3; z = 3; t[n_] := t[n] = NestList[Sort[Flatten[Table[Map[Join[#, {m + Last[#]}] &, #], {m, width}], 1]] &, {{1}}, n]
Column[Table[t[n], {n, 1, z}]] (*1st z generations*)
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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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STATUS
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approved
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