A267539 Decimal representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.
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
Offset: 0
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 sequences related to cellular automata
- Index to Elementary Cellular Automata
Programs
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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 *) -
PARI
a(n) = bitneg(3<<(n-3),n+1); \\ Kevin Ryde, Apr 15 2022
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