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 A266982 Triangle read by rows giving successive states of cellular automaton generated by "Rule 81" initiated with a single ON (black) cell. 3
 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Row n has length 2n+1. This sequence is also generated by rule 113. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science FORMULA Conjecture: a(0)=1; for n>0, a(n) = ( Sum_{i=1..n-2} floor((n-2)/i) ) mod 2. - Wesley Ivan Hurt, Mar 22 2016 EXAMPLE The first ten rows:                   1                 0 0 1               1 1 0 0 0             0 0 1 1 1 1 1           1 1 0 0 0 0 0 0 0         0 0 1 1 1 1 1 1 1 1 1       1 1 0 0 0 0 0 0 0 0 0 0 0     0 0 1 1 1 1 1 1 1 1 1 1 1 1 1   1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 MATHEMATICA rule=81; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *) CROSSREFS Sequence in context: A188398 A288929 A285083 * A051341 A057211 A120531 Adjacent sequences:  A266979 A266980 A266981 * A266983 A266984 A266985 KEYWORD nonn,tabf,easy AUTHOR Robert Price, Jan 07 2016 STATUS approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)