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A075437
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Triangle read by rows giving successive iterations of the Rule 110 elementary cellular automaton starting with a single black (1) cell where row n is of length 2n+1.
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6
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1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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The right n terms in a(n) are all 0.
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REFERENCES
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S. Wolfram, A New Kind of Science. Champaign, IL: Wolfram Media, p. 31ff, 2002.
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LINKS
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Eric Weisstein's World of Mathematics, Rule 110
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EXAMPLE
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1;
1,1,0;
1,1,1,0,0;
1,1,0,1,0,0,0; ...
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MATHEMATICA
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A075437list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[110, {{1}, 0}, {rowmax, All}]]; A075437list[10] (* Generates 11 rows *) (* Paolo Xausa, Oct 04 2023 *)
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PROG
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(Haskell)
a075437 n k = a075437_tabf !! n !! k
a075437_row n = a075437_tabf !! n
a075437_tabf = iterate rule110 [1] where
rule110 row = f ([0, 0] ++ row ++ [0, 0]) where
f [_, _] = []
f (_:ws@(0:0:_)) = 0 : f ws
f (1:ws@(1:1:_)) = 0 : f ws
f (_:ws@(_:_:_)) = 1 : f ws
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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