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A319610
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a(n) is the minimal number of successive OFF cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell.
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2
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0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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0,3
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COMMENTS
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OFF cells outside the triangle of active cells are ignored.
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LINKS
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FORMULA
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G.f.: x (x + x/(1 - x) + x^3 + x^5 + x^7) (conjectured).
For n > 9, a(n)=1 at least up to n = 20000.
It is conjectured that for all n>=10, a(n)=1.
A period-4 pattern of length-1 runs starting at row 26 forces a(n) = 1 for all n >= 26 (see image). - Charlie Neder, Dec 15 2018
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EXAMPLE
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The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
1 . a(1)= (0)
2 . . . a(2)= (0)
3 . . 0 0 . a(3)= (2)
4 . . 0 . . . . a(4)= (1)
5 . . 0 0 . 0 0 0 . a(5)= (2)
6 . . 0 . . . . 0 . . . a(6)= (1)
7 . . 0 0 . 0 0 0 0 . 0 0 . a(7)= (2)
8 . . 0 . . . . 0 0 . . . . . . a(8)= (1)
9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 . a(9)= (2)
10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . . a(10)=(1)
11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 . a(11)=(1)
12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . . a(12)=(1)
13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 . a(13)=(1)
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MATHEMATICA
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CellularAutomaton[30, {{1}, 0}, 200];
(Reverse[Internal`DeleteTrailingZeros[Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
Table[Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Min, {i, 1, % // Length}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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