A267536 Decimal representation of the n-th iteration of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 25, 103, 415, 1663, 6655, 26623, 106495, 425983, 1703935, 6815743, 27262975, 109051903, 436207615, 1744830463, 6979321855, 27917287423, 111669149695, 446676598783, 1786706395135, 7146825580543, 28587302322175, 114349209288703, 457396837154815

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 sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 17 2016 and Apr 20 2019: (Start)

a(n) = 5*a(n-1) - 4*a(n-2) for n > 3.

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

(End)

Empirical a(n) = 13*2^(2*n-3) - 1 for n > 1. - Colin Barker, Nov 25 2016 and Apr 20 2019

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, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, rows}]   (* Decimal Representation of Rows *)

Prog

(PARI) a(n) = n<<=1; bitneg(6<<(n-4), n+1); \\ Kevin Ryde, Apr 25 2022

Crossrefs

Cf. A267533, A267535.

Sequence in context: A253220 A037481 A199844 * A029871 A188178 A147543

Adjacent sequences: A267533 A267534 A267535 * A267537 A267538 A267539

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved