%I #25 Jun 13 2022 14:52:48

%S 1,5,10,99,124,1935,496,32319,1984,522495,7936,8381439,31744,

%T 134189055,126976,2147368959,507904,34359279615,2031616,549753978879,

%U 8126464,8796085682175,32505856,140737458995199,130023424,2251799696244735,520093696,36028796549201919

%N Decimal representation of the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267042/b267042.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 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%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 10 2016: (Start)

%F a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>8.

%F G.f.: (1+5*x-11*x^2-6*x^3-2*x^4+276*x^5-1332*x^6-320*x^7+1344*x^8) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

%F (End)

%t rule=91; 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 *) Table[FromDigits[catri[[k]],2],{k,1,rows}] (* Decimal Representation of Rows *)

%Y Cf. A267015, A267041.

%K nonn

%O 0,2

%A _Robert Price_, Jan 09 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022