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 A266220 Number of ON (black) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 2, 0, 7, 0, 11, 0, 15, 0, 19, 0, 23, 0, 27, 0, 31, 0, 35, 0, 39, 0, 43, 0, 47, 0, 51, 0, 55, 0, 59, 0, 63, 0, 67, 0, 71, 0, 75, 0, 79, 0, 83, 0, 87, 0, 91, 0, 95, 0, 99, 0, 103, 0, 107, 0, 111, 0, 115, 0, 119, 0, 123, 0, 127, 0, 131, 0, 135, 0, 139, 0 (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 Index entries for sequences related to cellular automata Index to Elementary Cellular Automata FORMULA Conjectures from Colin Barker, Dec 25 2015 and Apr 13 2019: (Start) a(n) = 1/2*(1-(-1)^n)*(2*n+1) for n>1. a(n) = 2*a(n-2) - a(n-4) for n>5. G.f.: (1+2*x-2*x^2+3*x^3+x^4-x^5) / ((1-x)^2*(1+x)^2). (End) 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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *) CROSSREFS Cf. A266216. Sequence in context: A269430 A363891 A142709 * A022897 A192496 A156442 Adjacent sequences: A266217 A266218 A266219 * A266221 A266222 A266223 KEYWORD nonn,easy AUTHOR Robert Price, Dec 24 2015 STATUS approved

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Last modified December 2 19:54 EST 2023. Contains 367526 sequences. (Running on oeis4.)