# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a266304 Showing 1-1 of 1 %I A266304 #22 Apr 15 2019 06:02:06 %S A266304 0,1,5,6,14,15,27,28,44,45,65,66,90,91,119,120,152,153,189,190,230, %T A266304 231,275,276,324,325,377,378,434,435,495,496,560,561,629,630,702,703, %U A266304 779,780,860,861,945,946,1034,1035,1127,1128,1224,1225,1325,1326,1430 %N A266304 Total number of OFF (white) cells after n iterations of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell. %D A266304 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. %H A266304 Robert Price, Table of n, a(n) for n = 0..999 %H A266304 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A266304 Index entries for sequences related to cellular automata %H A266304 Index to Elementary Cellular Automata %F A266304 Conjectures from _Colin Barker_, Dec 28 2015 and Apr 15 2019: (Start) %F A266304 a(n) = n*(n+(-1)^n+2)/2. %F A266304 a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4. %F A266304 G.f.: x*(1+4*x-x^2) / ((1-x)^3*(1+x)^2). (End) %F A266304 a(n) = Sum_{i=1..n} (n-i-1) mod 2. - _Wesley Ivan Hurt_, Sep 15 2017 %t A266304 rule=15; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *) %Y A266304 Cf. A266300. %K A266304 nonn,easy %O A266304 0,3 %A A266304 _Robert Price_, Dec 26 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE