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 A118109 Binary representation of n-th iteration of the Rule 54 elementary cellular automaton starting with a single black cell. 5
 1, 111, 10001, 1110111, 100010001, 11101110111, 1000100010001, 111011101110111, 10001000100010001, 1110111011101110111, 100010001000100010001, 11101110111011101110111, 1000100010001000100010001, 111011101110111011101110111, 10001000100010001000100010001, 1110111011101110111011101110111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..999 Eric Weisstein's World of Mathematics, Rule 54 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000). FORMULA From Colin Barker, Dec 08 2015: (Start) a(n) = 10001*a(n-2)-10000*a(n-4) for n>3. G.f.: (1+111*x) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)). (End) EXAMPLE From Michael De Vlieger, Oct 07 2015: (Start) First 8 rows, representing ON cells as "1", OFF cells within the bounds of ON cells as "0", interpreted as a binary number at left, the decimal equivalent appearing at right:                    1 =     1                  111 =     7               1 0001 =    17             111 0111 =   119          1 0001 0001 =   273        111 0111 0111 =  1911     1 0001 0001 0001 =  4369   111 0111 0111 0111 = 30583 10001 0001 0001 0001 = 69905 (End) MATHEMATICA rule=54; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}]   (* Binary Representation of Rows *)(* Robert Price, Feb 21 2016 *) PROG (PARI) Vec((1+111*x)/((1-x)*(1+x)*(1-100*x)*(1+100*x)) + O(x^20)) \\ Colin Barker, Dec 14 2015 CROSSREFS Cf. A071030 (essentially the same but lists bits separately), A118108 (converted to base 10). Sequence in context: A286771 A284208 A266381 * A265280 A267275 A135577 Adjacent sequences:  A118106 A118107 A118108 * A118110 A118111 A118112 KEYWORD nonn,tabf,easy AUTHOR Eric W. Weisstein, Apr 13 2006 EXTENSIONS Terms changed to match definition, as suggested by Michael De Vlieger. - N. J. A. Sloane, Oct 17 2015 STATUS approved

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