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A110266
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Number of blocks of ON cells in n-th row of triangle generated by Wolfram's "Rule 30".
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1
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1, 1, 2, 2, 3, 3, 4, 3, 4, 5, 6, 6, 7, 7, 8, 7, 7, 8, 10, 9, 9, 11, 14, 12, 11, 12, 15, 16, 14, 15, 17, 14, 15, 17, 20, 18, 18, 18, 21, 21, 17, 19, 21, 20, 23, 22, 23, 22, 23, 21, 27, 30, 26, 27, 29, 29, 28, 28, 33, 31, 30, 31, 36, 32, 28, 29, 33, 33, 33, 35
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OFFSET
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1,3
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COMMENTS
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Old name was "Number of trees appearing at n-th generation of a black cell following Wolfram's Rule 30 cellular automaton."
At each generation, "looking back", one can see "behind", groups (sort of black isles) of contiguous black cells which after a while appear to be trees growing. It should be possible to describe each one of them in terms of trees theory.
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LINKS
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Eric Weisstein's World of Mathematics, Rule 30.
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EXAMPLE
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a(1)=1 because one black cell;
a(2)=1 because there are now 3 contiguous black cell connected to the first one, which forms one only black surface;
a(3)=2 because two black cells are now connected to the preceding black surface and another black cell appears, which is isolated, so we have two separate black surfaces: 2.
Rule 30 triangle begins:
1
111
11 1
11 1111
11 1 1
11 1111 111
11 1 1 1
11 1111 111111
11 1 111 1
and the number of blocks of ON cells in each row is 1, 1, 2, 2, 3, 3, 4, 3, 4, ... (End)
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CROSSREFS
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Cf. A070950, A051023, A092539, A092540, A070952, A100053, A100054, A100055, A094603, A094604, A000225, A074890.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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