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 A255281 Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+1+y)-y/x-x. 2
 1, 7, 7, 31, 7, 49, 31, 127, 7, 49, 49, 217, 31, 217, 127, 511, 7, 49, 49, 217, 49, 343, 217, 889, 31, 217, 217, 961, 127, 889, 511, 2031, 7, 49, 49, 217, 49, 343, 217, 889, 49, 343, 343, 1519, 217, 1519, 889, 3577, 31, 217, 217, 961, 217, 1519 (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 367 (see Ekhad-Sloane-Zeilberger "Odd-Rule Cellular Automata on the Square Grid" link). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..8191 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 A255282. EXAMPLE Here is the neighborhood f: [0, X, X] [X, X, 0] [X, X, X] which contains a(1) = 7 ON cells. MATHEMATICA (* f = A255282 *) f=1; f=7; f=31; f=127; f=511; f=2031; f=8043; f=31735; f=125063; f[n_] := f[n] = 10 f[n-10] + 22 f[n-9] - 11 f[n-8] + 31 f[n-7] - 24 f[n-6] + 3 f[n-5] + 18 f[n-4] - 21 f[n-3] + 5 f[n-1]; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[] == 1&], {n, 0, 53}] (* Jean-François Alcover, Jul 12 2017 *) CROSSREFS Cf. A255282. Sequence in context: A246039 A186142 A188274 * A255283 A140252 A095343 Adjacent sequences:  A255278 A255279 A255280 * A255282 A255283 A255284 KEYWORD nonn AUTHOR N. J. A. Sloane and Doron Zeilberger, Feb 19 2015 STATUS approved

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Last modified August 25 15:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)