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 A255279 Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+1+y)-y/x-x*y. 2
 1, 7, 7, 25, 7, 49, 25, 107, 7, 49, 49, 175, 25, 175, 107, 413, 7, 49, 49, 175, 49, 343, 175, 749, 25, 175, 175, 625, 107, 749, 413, 1615, 7, 49, 49, 175, 49, 343, 175, 749, 49, 343, 343, 1225, 175, 1225, 749, 2891, 25, 175, 175, 625, 175, 1225 (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 277 (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 A255280. EXAMPLE Here is the neighborhood f: [0, X, 0] [X, X, X] [X, X, X] which contains a(1) = 7 ON cells. MATHEMATICA (* f = A255280 *) f=1; f=7; f=25; f=107; f=413; f=1615; f[n_] := f[n] = -16 f[n-7] - 16 f[n-6] + 16 f[n-4] - 9 f[n-3] - 3 f[n-2] + 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. A255280. Sequence in context: A289409 A290520 A247666 * A230496 A295733 A255277 Adjacent sequences:  A255276 A255277 A255278 * A255280 A255281 A255282 KEYWORD nonn AUTHOR N. J. A. Sloane and Doron Zeilberger, Feb 19 2015 STATUS approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)