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 A266286 Number of OFF (white) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 2, 3, 3, 6, 4, 9, 5, 12, 6, 15, 7, 18, 8, 21, 9, 24, 10, 27, 11, 30, 12, 33, 13, 36, 14, 39, 15, 42, 16, 45, 17, 48, 18, 51, 19, 54, 20, 57, 21, 60, 22, 63, 23, 66, 24, 69, 25, 72, 26, 75, 27, 78, 28, 81, 29, 84, 30, 87, 31, 90, 32, 93, 33, 96, 34, 99, 35 (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+2)*n-3*(-1)^n+3)/4. a(n) = 2*a(n-2)-a(n-4) for n>3. G.f.: x*(2+3*x-x^2) / ((1-x)^2*(1+x)^2). (End) Conjecture: a(n) = (n^2)mod(2n-3) for n>6. - Andres Cicuttin, Aug 29 2019 Conjecture: E.g.f.: (1/4)*exp(-x)*(- 3 - 2*x + exp(2*x)*(3 + 4*x)). - Stefano Spezia, Aug 31 2019 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 *) 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. A266282. Sequence in context: A049990 A173739 A062774 * A045892 A160791 A115973 Adjacent sequences:  A266283 A266284 A266285 * A266287 A266288 A266289 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2015 STATUS approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)