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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 Index entries for sequences related to cellular automata Index to Elementary Cellular Automata 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 June 6 20:05 EDT 2023. Contains 363151 sequences. (Running on oeis4.)