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A075437 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. 6
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)
OFFSET
0,1
COMMENTS
The right n terms in a(n) are all 0.
T(n,k) = A070887(n+1,k+1), k=0..n. - Reinhard Zumkeller, Jun 26 2013
REFERENCES
S. Wolfram, A New Kind of Science. Champaign, IL: Wolfram Media, p. 31ff, 2002.
LINKS
Eric Weisstein's World of Mathematics, Rule 110
EXAMPLE
1;
1,1,0;
1,1,1,0,0;
1,1,0,1,0,0,0; ...
MATHEMATICA
A075437list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[110, {{1}, 0}, {rowmax, All}]]; A075437list[10] (* Generates 11 rows *) (* Paolo Xausa, Oct 04 2023 *)
PROG
(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
-- Reinhard Zumkeller, Jun 26 2013
CROSSREFS
Cf. A070887.
Sequence in context: A342005 A354355 A266974 * A130047 A293233 A302050
KEYWORD
nonn,tabl
AUTHOR
Eric W. Weisstein, Sep 15 2002
STATUS
approved

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Last modified June 25 18:50 EDT 2024. Contains 373707 sequences. (Running on oeis4.)