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A267539 Decimal representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell. 3
1, 3, 6, 12, 25, 51, 103, 207, 415, 831, 1663, 3327, 6655, 13311, 26623, 53247, 106495, 212991, 425983, 851967, 1703935, 3407871, 6815743, 13631487, 27262975, 54525951, 109051903, 218103807, 436207615, 872415231, 1744830463, 3489660927, 6979321855 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 17 2016 and Apr 20 2019: (Start)
a(n) = 3*a(n-1)-2*a(n-2) for n > 4. [n range correction by Karl V. Keller, Jr., Apr 14 2022]
G.f.: (1-x^2+x^4) / ((1-x)*(1-2*x)).
(End)
{1,3,6} followed by A198274 (conjectured). - Robert Price, Jan 17 2016
MATHEMATICA
rule=143; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}] (* binary representation of middle column *)
PROG
(PARI) a(n) = bitneg(3<<(n-3), n+1); \\ Kevin Ryde, Apr 15 2022
CROSSREFS
Sequence in context: A077854 A265700 A293313 * A243722 A187260 A243723
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 16 2016
STATUS
approved

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Last modified February 28 00:18 EST 2024. Contains 370379 sequences. (Running on oeis4.)