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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 Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened Eric Weisstein's World of Mathematics, Rule 110 S. Wolfram, A New Kind of Science Index entries for sequences related to cellular automata Index to Elementary Cellular Automata 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 Adjacent sequences: A075434 A075435 A075436 * A075438 A075439 A075440 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.)