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 A266722 Number of ON (black) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 2, 2, 6, 2, 10, 2, 14, 2, 18, 2, 22, 2, 26, 2, 30, 2, 34, 2, 38, 2, 42, 2, 46, 2, 50, 2, 54, 2, 58, 2, 62, 2, 66, 2, 70, 2, 74, 2, 78, 2, 82, 2, 86, 2, 90, 2, 94, 2, 98, 2, 102, 2, 106, 2, 110, 2, 114, 2, 118, 2, 122, 2, 126, 2, 130, 2, 134, 2, 138, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n >= 3, also the number of maximum independent vertex sets in the n-prism graph. - Eric W. Weisstein, Mar 30 2017 For n >= 3, also the number of maximum independent edge sets in the n-web graph. - Eric W. Weisstein, Dec 31 2017 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximum Independent Edge Set Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set Eric Weisstein's World of Mathematics, Prism Graph Eric Weisstein's World of Mathematics, Web Graph S. Wolfram, A New Kind of Science FORMULA Conjectures from Colin Barker, Jan 05 2016 and Apr 17 2019: (Start) a(n) = 1+(-1)^n+n-(-1)^n*n for n>0. a(n) = 2*a(n-2)-a(n-4) for n>4. G.f.: (1+2*x-x^2)*(1+x^2) / ((1-x)^2*(1+x)^2). (End) MATHEMATICA rule=59; 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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *) CROSSREFS Cf. A266716. Sequence in context: A096869 A154009 A297792 * A232625 A099985 A298299 Adjacent sequences:  A266719 A266720 A266721 * A266723 A266724 A266725 KEYWORD nonn,easy AUTHOR Robert Price, Jan 03 2016 STATUS approved

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Last modified June 25 04:06 EDT 2019. Contains 324345 sequences. (Running on oeis4.)