%I #15 Apr 19 2019 05:13:32
%S 1,3,5,9,14,22,27,39,44,60,65,85,90,114,119,147,152,184,189,225,230,
%T 270,275,319,324,372,377,429,434,490,495,555,560,624,629,697,702,774,
%U 779,855,860,940,945,1029,1034,1122,1127,1219,1224,1320,1325,1425,1430
%N Total number of ON (black) cells after n iterations 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="/A267047/b267047.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 and Apr 19 2019: (Start)
%F a(n) = (n^2+4*n-(-1)^n*(n-3)-3)/2 for n>1.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>6.
%F G.f.: (1+2*x+2*x^4+2*x^5-3*x^6) / ((1-x)^3*(1+x)^2).
%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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc,k]],{k,1,rows}] (* Number of Black cells through stage n *)
%Y Cf. A267015.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 09 2016