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 A267271 Decimal representation of the n-th iteration of the "Rule 115" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 5, 12, 111, 96, 1919, 768, 31743, 6144, 516095, 49152, 8323071, 393216, 133693439, 3145728, 2143289343, 25165824, 34326183935, 201326592, 549487378431, 1610612736, 8793945538559, 12884901888, 140720308486143, 103079215104, 2251662374731775, 824633720832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. Index entries for linear recurrences with constant coefficients, signature (0,25,0,-152,0,128). FORMULA Conjectures from Colin Barker, Jan 14 2016 and Apr 19 2019: (Start) a(n) = 25*a(n-2) - 152*a(n-4) + 128*a(n-6) for n > 6. G.f.: (1 + 5*x - 13*x^2 - 14*x^3 - 52*x^4 - 96*x^5 + 64*x^6) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)). (End) MATHEMATICA rule=115; 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[FromDigits[catri[[k]], 2], {k, 1, rows}] (* decimal representation of rows *) CROSSREFS Cf. A267269, A267270. Sequence in context: A304001 A009731 A009427 * A009754 A096314 A332466 Adjacent sequences: A267268 A267269 A267270 * A267272 A267273 A267274 KEYWORD nonn,easy AUTHOR Robert Price, Jan 12 2016 STATUS approved

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Last modified January 29 01:41 EST 2023. Contains 359905 sequences. (Running on oeis4.)