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 A266287 Total number of OFF (white) cells after n iterations of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 2, 5, 8, 14, 18, 27, 32, 44, 50, 65, 72, 90, 98, 119, 128, 152, 162, 189, 200, 230, 242, 275, 288, 324, 338, 377, 392, 434, 450, 495, 512, 560, 578, 629, 648, 702, 722, 779, 800, 860, 882, 945, 968, 1034, 1058, 1127, 1152, 1224, 1250, 1325, 1352, 1430 (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) = (2*n^2+5*n+(-1)^n*(n-1)+1)/4. 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*(2+3*x-x^2) / ((1-x)^3*(1+x)^2). (End) MATHEMATICA rule=13; 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. A266282. Sequence in context: A191109 A190105 A295400 * A111711 A095348 A215725 Adjacent sequences:  A266284 A266285 A266286 * A266288 A266289 A266290 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2015 EXTENSIONS Conjectures from Colin Barker, Apr 14 2019 STATUS approved

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Last modified October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)