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 A265724 Total number of OFF (white) cells after n iterations of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell. 2
 0, 3, 7, 10, 18, 21, 33, 36, 52, 55, 75, 78, 102, 105, 133, 136, 168, 171, 207, 210, 250, 253, 297, 300, 348, 351, 403, 406, 462, 465, 525, 528, 592, 595, 663, 666, 738, 741, 817, 820, 900, 903, 987, 990, 1078, 1081, 1173, 1176, 1272, 1275, 1375, 1378, 1482 (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 16 2015 and Apr 16 2019: (Start) a(n) = 1/2*(n^2+(-1)^n*n+4*n-(-1)^n+1). a(n) = 1/2*(n^2+5*n) for n even. a(n) = 1/2*(n^2+3*n+2) for n odd. a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. G.f.: x*(3+4*x-3*x^2) / ((1-x)^3*(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, and the running total up to that row:                       .                        =  0  ->   0                     0 0 0                      =  3  ->   3                   0 0 . 0 0                    =  4  ->   7                 . . 0 0 0 . .                  =  3  ->  10               0 0 0 0 . 0 0 0 0                =  8  ->  18             . . . . 0 0 0 . . . .              =  3  ->  21           0 0 0 0 0 0 . 0 0 0 0 0 0            = 12  ->  33         . . . . . . 0 0 0 . . . . . .          =  3  ->  36       0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0        = 16  ->  52     . . . . . . . . 0 0 0 . . . . . . . .      =  3  ->  55   0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0    = 20  ->  75 . . . . . . . . . . 0 0 0 . . . . . . . . . .  =  3  ->  78 (End) MATHEMATICA rows = 53; Accumulate[Count[#, n_ /; n == 0] & /@ Table[Table[Take[CellularAutomaton[1, {{1}, 0}, rows - 1, {All, All}][[k]], {rows - k + 1, rows + k - 1}], {k, rows}][[k]], {k, 1, rows}]] (* Michael De Vlieger, Dec 14 2015 *) CROSSREFS Cf. A265718, A265720, A265721. Sequence in context: A042591 A098001 A171071 * A342448 A024330 A069153 Adjacent sequences:  A265721 A265722 A265723 * A265725 A265726 A265727 KEYWORD nonn,easy AUTHOR Robert Price, Dec 14 2015 STATUS approved

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)