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 A266589 Binary representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 10, 1110, 1000001, 111000, 11100000111, 11100000, 111110000011111, 1110000000, 1111111000001111111, 111000000000, 11111111100000111111111, 11100000000000, 111111111110000011111111111, 1110000000000000, 1111111111111000001111111111111, 111000000000000000 (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..1000 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 (0,10101,0,-1010100,0,1000000). FORMULA From Colin Barker, Jan 01 2016: (Start) a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>7. G.f.: (1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)). (End) MATHEMATICA rule=37; 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 *) PROG (PARI) Vec((1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)) + O(x^20)) \\ Colin Barker, Jan 01 2016 CROSSREFS Cf. A266588. Sequence in context: A001391 A049064 A267246 * A015026 A130598 A267595 Adjacent sequences:  A266586 A266587 A266588 * A266590 A266591 A266592 KEYWORD nonn,easy AUTHOR Robert Price, Jan 01 2016 STATUS approved

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)