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 A118108 Decimal representation of n-th iteration of the Rule 54 elementary cellular automaton starting with a single black cell. 6
 1, 7, 17, 119, 273, 1911, 4369, 30583, 69905, 489335, 1118481, 7829367, 17895697, 125269879, 286331153, 2004318071, 4581298449, 32069089143, 73300775185, 513105426295, 1172812402961, 8209686820727, 18764998447377, 131354989131639, 300239975158033 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(1660) is 1000 digits long. - Michael De Vlieger, Oct 07 2015 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..1660 A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata..., Fig 8. Eric Weisstein's World of Mathematics, Rule 54 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16). FORMULA a(n) = 7(4^(n+1)-1)/15 for n odd; a(n) = (4^(n+2)-1)/15 for n even. From Colin Barker, Oct 08 2015: (Start) a(n) = 17*a(n-2) - 16*a(n-4) for n>3. G.f.: (7*x+1) / ((x-1)*(x+1)*(4*x-1)*(4*x+1)). (End) EXAMPLE From Michael De Vlieger, Oct 07 2015: (Start) First 8 rows, representing ON cells as "1", OFF cells within the bounds of ON cells as "0", interpreted as a binary number at left, the decimal equivalent appearing at right:                     1 =     1                   111 =     7                1 0001 =    17              111 0111 =   119           1 0001 0001 =   273         111 0111 0111 =  1911      1 0001 0001 0001 =  4369    111 0111 0111 0111 = 30583 1 0001 0001 0001 0001 = 69905 (End) MATHEMATICA clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[54, {{1}, 0}, 27]] (* or *) Table[If[EvenQ@ n, (4^(n + 2) - 1), 7 (4^(n + 1) - 1)]/15, {n, 0, 27}] (* Michael De Vlieger, Oct 07 2015 *) PROG (PARI) Vec((7*x+1)/((x-1)*(x+1)*(4*x-1)*(4*x+1)) + O(x^30)) \\ Colin Barker, Oct 08 2015 CROSSREFS See A071030, A118109 for two other versions of this sequence. Sequence in context: A063384 A165246 A266382 * A227506 A244279 A214149 Adjacent sequences:  A118105 A118106 A118107 * A118109 A118110 A118111 KEYWORD nonn,tabf,base,easy AUTHOR Eric W. Weisstein, Apr 13 2006 EXTENSIONS a(23)-a(24) from Michael De Vlieger, Oct 07 2015 STATUS approved

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