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Total number of ON (black) cells after n iterations of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.
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%I #25 Nov 30 2020 08:14:10

%S 1,2,6,13,22,33,46,61,78,97,118,141,166,193,222,253,286,321,358,397,

%T 438,481,526,573,622,673,726,781,838,897,958,1021,1086,1153,1222,1293,

%U 1366,1441,1518,1597,1678,1761,1846,1933,2022,2113,2206,2301,2398,2497

%N Total number of ON (black) cells after n iterations of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.

%C With the exception of the first one or two entries the same as A123968 and A028872. - _R. J. Mathar_, Jan 24 2016

%H Robert Price, <a href="/A267874/b267874.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>, 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>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _Colin Barker_, Jan 22 2016 and Apr 20 2019: (Start)

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

%F G.f.: (1-x+3*x^2-x^4) / (1-x)^3.

%F (End)

%t rule=235; 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. A267869.

%Y Cf. A028872, A123968.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 21 2016