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 A266250 Total number of ON (black) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 1, 3, 5, 9, 14, 18, 27, 31, 44, 48, 65, 69, 90, 94, 119, 123, 152, 156, 189, 193, 230, 234, 275, 279, 324, 328, 377, 381, 434, 438, 495, 499, 560, 564, 629, 633, 702, 706, 779, 783, 860, 864, 945, 949, 1034, 1038, 1127, 1131, 1224, 1228, 1325, 1329, 1430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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) = (n^2-(-1)^n*(n-4)+2)/2 for n>2. a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7. G.f.: (1+2*x^3+x^4+x^5-2*x^6+x^7) / ((1-x)^3*(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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *) CROSSREFS Cf. A266243. Sequence in context: A211389 A288259 A082874 * A127720 A118002 A069533 Adjacent sequences:  A266247 A266248 A266249 * A266251 A266252 A266253 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 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)