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 A255275 Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+1+y)-y/x. 1
 1, 8, 8, 28, 8, 64, 28, 128, 8, 64, 64, 224, 28, 224, 128, 480, 8, 64, 64, 224, 64, 512, 224, 1024, 28, 224, 224, 784, 128, 1024, 480, 2008, 8, 64, 64, 224, 64, 512, 224, 1024, 64, 512, 512, 1792, 224, 1792, 1024, 3840, 28, 224, 224, 784, 224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the number of ON cells in a certain two-dimensional cellular automaton in which the neighborhood of a cell is defined by f, and in which a cell is ON iff there were an odd number of ON cells in the neighborhood at the previous generation. This is the odd-rule cellular automaton defined by OddRule 377 (see Ekhad-Sloane-Zeilberger "Odd-Rule Cellular Automata on the Square Grid" link). LINKS Shalosh B. Ekhad, N. J. A. Sloane, and  Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796, 2015; see also the Accompanying Maple Package. Shalosh B. Ekhad, N. J. A. Sloane, and  Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.04249, 2015. N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: Part 1, Part 2 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015 FORMULA This is the Run Length Transform of A255276. EXAMPLE Here is the neighborhood f: [0, X, X] [X, X, X] [X, X, X] which contains a(1) = 8 ON cells. MATHEMATICA (* f = A255276 *) f[0]=1; f[1]=8; f[2]=28; f[3]=128; f[4]=480; f[5]=2008; f[6]=7776; f[n_] := f[n] = -32f[n-8] - 24f[n-7] + 164f[n-6] - 236f[n-5] + 145f[n-4] - 24f[n-3] - 16f[n-2] + 8f[n-1]; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 52}] (* Jean-François Alcover, Jul 12 2017 *) CROSSREFS Cf. A255276. Sequence in context: A133038 A339734 A341834 * A253104 A122858 A143336 Adjacent sequences:  A255272 A255273 A255274 * A255276 A255277 A255278 KEYWORD nonn AUTHOR N. J. A. Sloane and Doron Zeilberger, Feb 19 2015 STATUS approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)