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 A271064 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 261", based on the 5-celled von Neumann neighborhood. 1
 7, -7, 47, -47, 119, -119, 223, -223, 359, -359, 527, -527, 727, -727, 959, -959, 1223, -1223, 1519, -1519, 1847, -1847, 2207, -2207, 2599, -2599, 3023, -3023, 3479, -3479, 3967, -3967, 4487, -4487, 5039, -5039, 5623, -5623, 6239, -6239, 6887, -6887, 7567 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Initialized with a single black (ON) cell at stage zero. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Robert Price, Table of n, a(n) for n = 0..127 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 FORMULA Conjectures from Chai Wah Wu, Dec 29 2016: (Start) a(n) = - a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) for n>4. G.f.: (-x^4 + 26*x^2 + 7)/((x - 1)^2*(x + 1)^3). (End) MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=261; stages=128; rule=IntegerDigits[code, 2, 10]; g=2*stages+1; (* Maximum size of grid *) a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *) ca=a; ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}]; PrependTo[ca, a]; (* Trim full grid to reflect growth by one cell at each stage *) k=(Length[ca[]]+1)/2; ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}]; on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *) CROSSREFS Cf. A271060. Sequence in context: A143430 A219399 A219447 * A173294 A165828 A161343 Adjacent sequences:  A271061 A271062 A271063 * A271065 A271066 A271067 KEYWORD sign,easy AUTHOR Robert Price, Mar 29 2016 STATUS approved

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Last modified July 23 11:18 EDT 2021. Contains 346259 sequences. (Running on oeis4.)