A267536 - OEIS

%I #31 Jul 06 2023 13:18:59

%S 1,6,25,103,415,1663,6655,26623,106495,425983,1703935,6815743,

%T 27262975,109051903,436207615,1744830463,6979321855,27917287423,

%U 111669149695,446676598783,1786706395135,7146825580543,28587302322175,114349209288703,457396837154815

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

%H Robert Price, <a href="/A267536/b267536.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Conjectures from _Colin Barker_, Jan 17 2016 and Apr 20 2019: (Start)

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

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

%F (End)

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

%t 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 *)

%o (PARI) a(n) = n<<=1; bitneg(6<<(n-4), n+1); \\ _Kevin Ryde_, Apr 25 2022

%Y Cf. A267533, A267535.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 16 2016