|
%I #16 Apr 16 2019 06:27:02
%S 1,2,4,7,11,17,21,31,35,49,53,71,75,97,101,127,131,161,165,199,203,
%T 241,245,287,291,337,341,391,395,449,453,511,515,577,581,647,651,721,
%U 725,799,803,881,885,967,971,1057,1061,1151,1155,1249,1253,1351,1355
%N Total number of ON (black) cells after n iterations of the "Rule 25" 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="/A266448/b266448.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_, Dec 30 2015 and Apr 16 2019: (Start)
%F a(n) = (2*n^2+2*n+(-1)^n*(7-2*n)+5)/4 for n>2.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7.
%F G.f.: (1+x+x^3+x^4+x^5-2*x^6+x^7) / ((1-x)^3*(1+x)^2).
%F (End)
%t rule=25; 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. A266441.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015
|
