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 A265225 Total number of ON (black) cells after n iterations of the "Rule 54" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 4, 6, 12, 15, 24, 28, 40, 45, 60, 66, 84, 91, 112, 120, 144, 153, 180, 190, 220, 231, 264, 276, 312, 325, 364, 378, 420, 435, 480, 496, 544, 561, 612, 630, 684, 703, 760, 780, 840, 861, 924, 946, 1012, 1035, 1104, 1128, 1200, 1225, 1300, 1326, 1404, 1431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Take the first 2n positive integers and choose n of them such that their sum: a) is divisible by n, and b) is minimal. It seems their sum equals a(n). - Ivan N. Ianakiev, Feb 16 2019 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 08 2015 and Apr 20 2019: (Start) a(n) = (n+1)*(2*n -(-1)^n +5)/4. a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. G.f.: (1+3*x) / ((1-x)^3*(1+x)^2). (End) a(n) = n + 1 + (n+1) * floor((n+1)/2), conjectured. - Wesley Ivan Hurt, Dec 25 2016 EXAMPLE From Michael De Vlieger, Dec 14 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                      =  2 ->  6                   1 1 1 . 1 1 1                    =  6 -> 12                 1 . . . 1 . . . 1                  =  3 -> 15               1 1 1 . 1 1 1 . 1 1 1                =  9 -> 24             1 . . . 1 . . . 1 . . . 1              =  4 -> 28           1 1 1 . 1 1 1 . 1 1 1 . 1 1 1            = 12 -> 40         1 . . . 1 . . . 1 . . . 1 . . . 1          =  5 -> 45       1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1        = 15 -> 60     1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1      =  6 -> 66   1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1    = 18 -> 84 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1  =  7 -> 91 (End) MAPLE A265225:=n->1/4*(n+1)*(2*n-(-1)^n+5): seq(A265225(n), n=0..60); # Wesley Ivan Hurt, Dec 25 2016 MATHEMATICA rule = 54; 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[Total /@ CellularAutomaton[54, {{1}, 0}, 52]] CROSSREFS Cf. A071030, A118108, A118109, A133872. Sequence in context: A256241 A247632 A104236 * A122781 A153355 A310597 Adjacent sequences:  A265222 A265223 A265224 * A265226 A265227 A265228 KEYWORD nonn,easy AUTHOR Robert Price, Dec 05 2015 STATUS approved

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Last modified August 22 11:34 EDT 2019. Contains 326176 sequences. (Running on oeis4.)