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 A265723 Number of OFF (white) cells in the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell. 2
 0, 3, 4, 3, 8, 3, 12, 3, 16, 3, 20, 3, 24, 3, 28, 3, 32, 3, 36, 3, 40, 3, 44, 3, 48, 3, 52, 3, 56, 3, 60, 3, 64, 3, 68, 3, 72, 3, 76, 3, 80, 3, 84, 3, 88, 3, 92, 3, 96, 3, 100, 3, 104, 3, 108, 3, 112, 3, 116, 3, 120, 3, 124, 3, 128, 3, 132, 3, 136, 3, 140, 3 (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 FORMULA Conjectures from Colin Barker, Dec 15 2015 and Apr 16 2019: (Start) a(n) = 1/2*((2*(-1)^n+2)*n-3*((-1)^n-1)). a(n) = 2*a(n-2) - a(n-4) for n>3. G.f.: x*(3+4*x-3*x^2) / ((1-x)^2*(1+x)^2). (End) EXAMPLE From Michael De Vlieger, Dec 14 2015: (Start) First 12 rows, replacing ones with "." for better visibility of OFF cells, followed by the total number of 0's per row at right:                       .                        =  0                     0 0 0                      =  3                   0 0 . 0 0                    =  4                 . . 0 0 0 . .                  =  3               0 0 0 0 . 0 0 0 0                =  8             . . . . 0 0 0 . . . .              =  3           0 0 0 0 0 0 . 0 0 0 0 0 0            = 12         . . . . . . 0 0 0 . . . . . .          =  3       0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0        = 16     . . . . . . . . 0 0 0 . . . . . . . .      =  3   0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0    = 20 . . . . . . . . . . 0 0 0 . . . . . . . . . .  =  3 (End) MATHEMATICA rows = 71; Count[#, n_ /; n == 0] & /@ Table[Table[Take[CellularAutomaton[1, {{1}, 0}, rows - 1, {All, All}][[k]], {rows - k + 1, rows + k - 1}], {k, 1, rows}][[k]], {k, 1, rows}] (* Michael De Vlieger, Dec 14 2015 *) CROSSREFS Cf. A265718, A265720, A265721. Sequence in context: A163108 A077005 A328347 * A134065 A015887 A077628 Adjacent sequences:  A265720 A265721 A265722 * A265724 A265725 A265726 KEYWORD nonn,easy AUTHOR Robert Price, Dec 14 2015 STATUS approved

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Last modified June 14 15:36 EDT 2021. Contains 345025 sequences. (Running on oeis4.)