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 A266068 Binary representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 100, 10, 1111001, 100, 11111110011, 1000, 111111111100111, 10000, 1111111111111001111, 100000, 11111111111111110011111, 1000000, 111111111111111111100111111, 10000000, 1111111111111111111111001111111, 100000000, 11111111111111111111111110011111111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Rule 35 also generates this sequence. LINKS Robert Price, Table of n, a(n) for n = 0..999 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. Index entries for linear recurrences with constant coefficients, signature (0,10011,0,-110010,0,100000). FORMULA G.f.: (1+100*x-10001*x^2+109901*x^3+10000*x^4-120000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)). - Colin Barker, Dec 21 2015 a(n) = (10*100^n - 99*10^((n-1)/2) - 1)/9 for odd n; a(n) = 10^(n/2) for even n. - Karl V. Keller, Jr., Aug 26 2021 EXAMPLE From Michael De Vlieger, Dec 21 2015: (Start) First 8 rows, replacing leading zeros with ".", the row converted to its binary equivalent at right:               1                =               1             1 0 0              =             100           . . . 1 0            =              10         1 1 1 1 0 0 1          =         1111001       . . . . . . 1 0 0        =             100     1 1 1 1 1 1 1 0 0 1 1      =     11111110011   . . . . . . . . . 1 0 0 0    =            1000 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1  = 111111111100111 (End) MATHEMATICA rule = 3; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}] PROG (Python) print([(10*100**n - 99*10**((n-1)//2) - 1)//9 if n%2 else 10**(n//2) for n in range(30)]) # Karl V. Keller, Jr., Aug 26 2021 CROSSREFS Cf. A263428, A266069. Sequence in context: A273479 A333399 A069037 * A285648 A084484 A231891 Adjacent sequences:  A266065 A266066 A266067 * A266069 A266070 A266071 KEYWORD nonn,easy AUTHOR Robert Price, Dec 20 2015 STATUS approved

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Last modified August 11 10:15 EDT 2022. Contains 356065 sequences. (Running on oeis4.)