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%I #18 Apr 18 2019 07:45:35
%S 1,4,8,13,20,27,37,46,59,70,86,99,118,133,155,172,197,216,244,265,296,
%T 319,353,378,415,442,482,511,554,585,631,664,713,748,800,837,892,931,
%U 989,1030,1091,1134,1198,1243,1310,1357,1427,1476,1549,1600,1676,1729
%N Total number of ON (black) cells after n iterations of the "Rule 158" 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="/A265382/b265382.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</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 07 2015 and Apr 18 2019: (Start)
%F a(n) = 1/16*(10*n^2+2*(-1)^n*n+34*n-3*(-1)^n+19).
%F a(n) = 1/16*(10*n^2+36*n+16) for n even.
%F a(n) = 1/16*(10*n^2+32*n+22) for n odd.
%F a(n) = 2*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4.
%F G.f.: (1+3*x+2*x^2-x^3) / ((1-x)^3*(1+x)^2).
%F (End)
%e From _Michael De Vlieger_, Dec 09 2015: (Start)
%e First 12 rows, replacing "0" with "." for better visibility of ON cells, followed by the total number of 1's per row, and the running total up to that row:
%e 1 = 1 -> 1
%e 1 1 1 = 3 -> 4
%e 1 1 1 . 1 = 4 -> 8
%e 1 1 1 . . 1 1 = 5 -> 13
%e 1 1 1 . 1 1 1 . 1 = 7 -> 20
%e 1 1 1 . . 1 1 . . 1 1 = 7 -> 27
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 = 10 -> 37
%e 1 1 1 . . 1 1 . . 1 1 . . 1 1 = 9 -> 46
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 = 13 -> 59
%e 1 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1 = 11 -> 70
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 = 16 -> 86
%e 1 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1 = 13 -> 99
%e 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 = 19 -> 118
%e (End)
%t rule = 158; rows = 30; Table[Total[Take[Table[Total[Table[Take[CellularAutomaton[rule,{{1},0},rows-1,{All,All}][[k]],{rows-k+1,rows+k-1}],{k,1,rows}][[k]]],{k,1,rows}],k]],{k,1,rows}]
%t Accumulate[Count[#, n_ /; n == 1] & /@ CellularAutomaton[158, {{1}, 0}, 51]] (* _Michael De Vlieger_, Dec 09 2015 *)
%Y Cf. A071037.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 07 2015