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 A269713 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood. 1
 1, 5, 13, 25, 45, 69, 113, 141, 193, 249, 353, 409, 513, 625, 837, 897, 1013, 1133, 1365, 1485, 1717, 1957, 2421, 2541, 2773, 3013, 3477, 3717, 4181, 4661, 5593, 5717, 5961, 6209, 6697, 6945, 7433, 7929, 8905, 9153, 9641, 10137, 11113, 11609, 12585, 13577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Initialized with a single black (ON) cell at stage zero. Rules 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692 and 700 also generate this sequence. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Robert Price, Table of n, a(n) for n = 0..300 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015. Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata MATHEMATICA rule=20; stages=300; ca=CellularAutomaton[{rule, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *) CROSSREFS Cf. A269711. Sequence in context: A102724 A147031 A147220 * A196069 A147182 A146175 Adjacent sequences: A269710 A269711 A269712 * A269714 A269715 A269716 KEYWORD nonn,easy AUTHOR Robert Price, Mar 04 2016 STATUS approved

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Last modified March 4 04:21 EST 2024. Contains 370522 sequences. (Running on oeis4.)