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 A266252 Total number of OFF (white) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 3, 6, 11, 16, 22, 31, 37, 50, 56, 73, 79, 100, 106, 131, 137, 166, 172, 205, 211, 248, 254, 295, 301, 346, 352, 401, 407, 460, 466, 523, 529, 590, 596, 661, 667, 736, 742, 815, 821, 898, 904, 985, 991, 1076, 1082, 1171, 1177, 1270, 1276, 1373, 1379, 1480 (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 28 2015 and Apr 14 2019: (Start) a(n) = ((-1)^n*(n-4)+n*(n+4))/2 for n>2. a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7. G.f.: x*(3+3*x-x^2-x^3-x^4+2*x^5-x^6) / ((1-x)^3*(1+x)^2). (End) MATHEMATICA rule=9; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *) CROSSREFS Cf. A266243. Sequence in context: A111582 A024401 A333709 * A267260 A116940 A278100 Adjacent sequences:  A266249 A266250 A266251 * A266253 A266254 A266255 KEYWORD nonn,easy AUTHOR Robert Price, Dec 25 2015 EXTENSIONS Conjectures from Colin Barker, Apr 14 2019 STATUS approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)