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 A266257 Total number of ON (black) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 2, 4, 9, 11, 20, 22, 35, 37, 54, 56, 77, 79, 104, 106, 135, 137, 170, 172, 209, 211, 252, 254, 299, 301, 350, 352, 405, 407, 464, 466, 527, 529, 594, 596, 665, 667, 740, 742, 819, 821, 902, 904, 989, 991, 1080, 1082, 1175, 1177, 1274, 1276, 1377, 1379 (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 27 2015 and Apr 14 2019: (Start) a(n) = ((n+1)^2-(-1)^n*(n-1))/2. a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4. G.f.: (1+x+3*x^3-x^4) / ((1-x)^3*(1+x)^2). (End) MATHEMATICA rule=11; 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 *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *) CROSSREFS Cf. A266253. Sequence in context: A047348 A186699 A093859 * A115905 A292769 A307997 Adjacent sequences:  A266254 A266255 A266256 * A266258 A266259 A266260 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 March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)