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 A266285 Number of ON (black) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 1, 2, 4, 3, 7, 4, 10, 5, 13, 6, 16, 7, 19, 8, 22, 9, 25, 10, 28, 11, 31, 12, 34, 13, 37, 14, 40, 15, 43, 16, 46, 17, 49, 18, 52, 19, 55, 20, 58, 21, 61, 22, 64, 23, 67, 24, 70, 25, 73, 26, 76, 27, 79, 28, 82, 29, 85, 30, 88, 31, 91, 32, 94, 33, 97, 34 (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) = ((-1)^n*(3-2*n)+4*n+1)/4. a(n) = 2*a(n-2)-a(n-4) for n>3. G.f.: (1+x+2*x^3) / ((1-x)^2*(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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *) CROSSREFS Cf. A266282. Sequence in context: A181049 A007203 A110412 * A258851 A194031 A064357 Adjacent sequences:  A266282 A266283 A266284 * A266286 A266287 A266288 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 January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)