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 A265430 Number of OFF (white) cells in the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell. 2
 0, 1, 3, 3, 5, 6, 8, 8, 10, 11, 13, 13, 15, 16, 18, 18, 20, 21, 23, 23, 25, 26, 28, 28, 30, 31, 33, 33, 35, 36, 38, 38, 40, 41, 43, 43, 45, 46, 48, 48, 50, 51, 53, 53, 55, 56, 58, 58, 60, 61, 63, 63, 65, 66, 68, 68, 70, 71, 73, 73, 75, 76, 78, 78, 80, 81, 83 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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*(10*n+3*(-1)^n-(1-i)*(-i)^n-(1+i)*i^n-1) where i = sqrt(-1). a(n) = a(n-1) + a(n-4) - a(n-5) for n>4. G.f.: x*(1+2*x+2*x^3) / ((1-x)^2*(1+x)*(1+x^2)). (End) EXAMPLE From Michael De Vlieger, Dec 09 2015: (Start) First 12 rows, replacing "1" with "." for better visibility of OFF cells, with total number of 0's in the row to the right of the chart:                       .                        =  0                     . . 0                      =  1                   . 0 . 0 0                    =  3                 . . . . 0 0 0                  =  3               . . . 0 . 0 0 0 0                =  5             . . 0 . . . 0 0 0 0 0              =  6           . 0 . . . 0 . 0 0 0 0 0 0            =  8         . . . . 0 . . . 0 0 0 0 0 0 0          =  8       . . . 0 . . . 0 . 0 0 0 0 0 0 0 0        = 10     . . 0 . . . 0 . . . 0 0 0 0 0 0 0 0 0      = 11   . 0 . . . 0 . . . 0 . 0 0 0 0 0 0 0 0 0 0    = 13 . . . . 0 . . . 0 . . . 0 0 0 0 0 0 0 0 0 0 0  = 13 (End) MATHEMATICA lim = 134; a = {}; Do[AppendTo[a, Take[#[[k]], 2 (k - 1) + 1]], {k, Floor[Length[#]/2]}] &@ CellularAutomaton[188, {{1}, 0}, lim]; Count[#, n_ /; n == 0] & /@ a (* Michael De Vlieger, Dec 09 2015 *) PROG (PARI) concat(0, Vec(x*(1+2*x+2*x^3)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100))) \\ Colin Barker, Dec 14 2015 CROSSREFS Cf. A118174. Sequence in context: A116592 A152772 A089175 * A262355 A138373 A011976 Adjacent sequences:  A265427 A265428 A265429 * A265431 A265432 A265433 KEYWORD nonn,easy AUTHOR Robert Price, Dec 08 2015 STATUS approved

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Last modified September 23 13:55 EDT 2017. Contains 292358 sequences.