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 A140252 Inverse binomial transform of A140420. 2
 0, 1, 1, 7, 7, 31, 31, 127, 127, 511, 511, 2047, 2047, 8191, 8191, 32767, 32767, 131071, 131071, 524287, 524287, 2097151, 2097151, 8388607, 8388607, 33554431, 33554431, 134217727, 134217727, 536870911, 536870911 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 673", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 23 2017 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 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 Wolfram Research, Wolfram Atlas of Simple Programs Index entries for linear recurrences with constant coefficients, signature (1, 4, -4). FORMULA a(2n+1) = a(2n+2)= A083420(n). a(n+1)-2a(n) = (-1)^n*A014551(n), n>0. a(n+1)-2a(n)-1 = 2*(-1)^n*A131577(n). O.g.f.: x(1+2x^2)/((2x-1)(1+2x)(x-1)). - R. J. Mathar, Aug 02 2008 a(n) = a(n-1)+4*a(n-2)-4*a(n-3), a(0)=0, a(1)=1, a(2)=1, a(3)=7. - Harvey P. Dale, May 28 2012 MATHEMATICA Join[{0}, LinearRecurrence[{1, 4, -4}, {1, 1, 7}, 30]] (* Harvey P. Dale, May 28 2012 *) CROSSREFS Sequence in context: A188274 A255281 A255283 * A095343 A286830 A286862 Adjacent sequences:  A140249 A140250 A140251 * A140253 A140254 A140255 KEYWORD nonn AUTHOR Paul Curtz, Jun 23 2008 EXTENSIONS Edited and extended by R. J. Mathar, Aug 02 2008 STATUS approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)