|
%I #17 Apr 18 2019 09:45:41
%S 1,2,5,7,10,16,19,29,32,46,49,67,70,92,95,121,124,154,157,191,194,232,
%T 235,277,280,326,329,379,382,436,439,497,500,562,565,631,634,704,707,
%U 781,784,862,865,947,950,1036,1039,1129,1132,1226,1229,1327,1330,1432
%N Total number of ON (black) cells after n iterations of the "Rule 37" 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="/A266594/b266594.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 02 2016 and Apr 18 2019: (Start)
%F a(n) = (n^2-(-1)^n*(n-3)+5)/2 for n>0.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.
%F G.f.: (1+x+x^2-2*x^4+3*x^5) / ((1-x)^3*(1+x)^2).
%F (End)
%t rule=37; 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. A266588.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 01 2016
|
