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 A266251 Number of OFF (white) cells in the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 3, 3, 5, 5, 6, 9, 6, 13, 6, 17, 6, 21, 6, 25, 6, 29, 6, 33, 6, 37, 6, 41, 6, 45, 6, 49, 6, 53, 6, 57, 6, 61, 6, 65, 6, 69, 6, 73, 6, 77, 6, 81, 6, 85, 6, 89, 6, 93, 6, 97, 6, 101, 6, 105, 6, 109, 6, 113, 6, 117, 6, 121, 6, 125, 6, 129, 6, 133, 6, 137, 6 (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*(-1)^n*n+2*n-9*(-1)^n+3)/2 for n>3. a(n) = 2*a(n-2)-a(n-4) for n>7. G.f.: x*(3+3*x-x^2-x^3-x^4+2*x^5-x^6) / ((1-x)^2*(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 *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *) CROSSREFS Cf. A266243. Sequence in context: A067782 A318916 A035299 * A021302 A004649 A002374 Adjacent sequences:  A266248 A266249 A266250 * A266252 A266253 A266254 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 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)