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 A265428 Number of ON (black) cells in the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 2, 2, 4, 4, 5, 5, 7, 7, 8, 8, 10, 10, 11, 11, 13, 13, 14, 14, 16, 16, 17, 17, 19, 19, 20, 20, 22, 22, 23, 23, 25, 25, 26, 26, 28, 28, 29, 29, 31, 31, 32, 32, 34, 34, 35, 35, 37, 37, 38, 38, 40, 40, 41, 41, 43, 43, 44, 44, 46, 46, 47, 47, 49, 49, 50, 50 (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, Elementary Cellular Automaton Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Colin Barker, Dec 09 2015: (Start) a(n) = 1/8*(6*n-3*(-1)^n+(1-i)*(-i)^n+(1+i)*i^n+9) where i = sqrt(-1). a(n) = a(n-1) + a(n-4) - a(n-5) for n > 4. G.f.: (1+x+2*x^3-x^4) / ((1-x)^2*(1+x)*(1+x^2)). (End) a(n) = (6*n+9+2*cos(n*Pi/2)-3*cos(n*Pi)-2*sin(n*Pi/2))/8. - Wesley Ivan Hurt, Oct 02 2017 EXAMPLE From Michael De Vlieger, Dec 09 2015: (Start) First 12 rows, replacing "0" with ".", ignoring "0" outside of range of 1's for better visibility of ON cells, with total number of 1's in the row to the left of the chart: 1  =   1 2  =   1 1 2  =   1 . 1 4  =   1 1 1 1 4  =   1 1 1 . 1 5  =   1 1 . 1 1 1 5  =   1 . 1 1 1 . 1 7  =   1 1 1 1 . 1 1 1 7  =   1 1 1 . 1 1 1 . 1 8  =   1 1 . 1 1 1 . 1 1 1 8  =   1 . 1 1 1 . 1 1 1 . 1 10 =   1 1 1 1 . 1 1 1 . 1 1 1 10 =   1 1 1 . 1 1 1 . 1 1 1 . 1 (End) MATHEMATICA rule = 188; rows = 30; Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}] Count[#, n_ /; n == 1] & /@ CellularAutomaton[188, {{1}, 0}, 66] (* Michael De Vlieger, Dec 09 2015 *) PROG (PARI) Vec((1+x+2*x^3-x^4)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100)) \\ Colin Barker, Dec 14 2015 CROSSREFS Cf. A118174. Sequence in context: A152850 A036714 A260734 * A035644 A288773 A288774 Adjacent sequences:  A265425 A265426 A265427 * A265429 A265430 A265431 KEYWORD nonn,easy AUTHOR Robert Price, Dec 08 2015 STATUS approved

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Last modified August 19 21:39 EDT 2018. Contains 313897 sequences. (Running on oeis4.)