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 A265382 Total number of ON (black) cells after n iterations of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 4, 8, 13, 20, 27, 37, 46, 59, 70, 86, 99, 118, 133, 155, 172, 197, 216, 244, 265, 296, 319, 353, 378, 415, 442, 482, 511, 554, 585, 631, 664, 713, 748, 800, 837, 892, 931, 989, 1030, 1091, 1134, 1198, 1243, 1310, 1357, 1427, 1476, 1549, 1600, 1676, 1729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..999 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton FORMULA Conjectures from Colin Barker, Dec 07 2015 and Apr 18 2019: (Start) a(n) = 1/16*(10*n^2+2*(-1)^n*n+34*n-3*(-1)^n+19). a(n) = 1/16*(10*n^2+36*n+16) for n even. a(n) = 1/16*(10*n^2+32*n+22) for n odd. a(n) = 2*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4. G.f.: (1+3*x+2*x^2-x^3) / ((1-x)^3*(1+x)^2). (End) EXAMPLE From Michael De Vlieger, Dec 09 2015: (Start) 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:                         1                          =  1 ->   1                       1 1 1                        =  3 ->   4                     1 1 1 . 1                      =  4 ->   8                   1 1 1 . . 1 1                    =  5 ->  13                 1 1 1 . 1 1 1 . 1                  =  7 ->  20               1 1 1 . . 1 1 . . 1 1                =  7 ->  27             1 1 1 . 1 1 1 . 1 1 1 . 1              = 10 ->  37           1 1 1 . . 1 1 . . 1 1 . . 1 1            =  9 ->  46         1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1          = 13 ->  59       1 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1        = 11 ->  70     1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1      = 16 ->  86   1 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1 . . 1 1    = 13 ->  99 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1  = 19 -> 118 (End) MATHEMATICA 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}] Accumulate[Count[#, n_ /; n == 1] & /@ CellularAutomaton[158, {{1}, 0}, 51]] (* Michael De Vlieger, Dec 09 2015 *) CROSSREFS Cf. A071037. Sequence in context: A312216 A312217 A312218 * A056738 A170907 A143978 Adjacent sequences:  A265379 A265380 A265381 * A265383 A265384 A265385 KEYWORD nonn,easy AUTHOR Robert Price, Dec 07 2015 STATUS approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)