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 A266221 Total number of ON (black) cells after n iterations of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 3, 3, 10, 10, 21, 21, 36, 36, 55, 55, 78, 78, 105, 105, 136, 136, 171, 171, 210, 210, 253, 253, 300, 300, 351, 351, 406, 406, 465, 465, 528, 528, 595, 595, 666, 666, 741, 741, 820, 820, 903, 903, 990, 990, 1081, 1081, 1176, 1176, 1275, 1275, 1378, 1378 (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..499 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton FORMULA Conjectures from Colin Barker, Dec 25 2015 and Apr 13 2019: (Start) a(n) = 1/2*(n+1)*(n-(-1)^n+1). a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5. G.f.: (1+2*x-2*x^2+3*x^3+x^4-x^5) / ((1-x)^3*(1+x)^2). (End) a(n) = A000217(A052928(n+1)) for n>0. - Michel Marcus, Sep 25 2016 MATHEMATICA rule=7; 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. A266216. Sequence in context: A057210 A278832 A168376 * A073709 A085288 A124630 Adjacent sequences:  A266218 A266219 A266220 * A266222 A266223 A266224 KEYWORD nonn,easy AUTHOR Robert Price, Dec 24 2015 EXTENSIONS Conjectures from Colin Barker, Apr 13 2019 STATUS approved

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Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)