A267157 Decimal representation of the middle column of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 4, 9, 19, 39, 79, 159, 319, 639, 1278, 2557, 5114, 10229, 20458, 40917, 81834, 163669, 327338, 654677, 1309354, 2618709, 5237418, 10474837, 20949674, 41899349, 83798698, 167597397, 335194794, 670389589, 1340779178, 2681558357, 5363116714, 10726233429

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..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 11 2016 and Apr 19 2019: (Start)

a(n) = (-(-1)^n+959*2^(n-7)-3)/6 for n>7.

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4.

G.f.: (1-x^2+x^3+x^4-x^10) / ((1-x)*(1+x)*(1-2*x)).

(End)

Mathematica

rule=107; 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 *)

Crossrefs

Cf. A267152.

Sequence in context: A056186 A265387 A293322 * A054135 A171858 A099568

Adjacent sequences: A267154 A267155 A267156 * A267158 A267159 A267160

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved