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 A140253 a(2*n) = 2*(2*4^(n-1)-1) and a(2*n-1) = 2*4^(n-1)-1. 5
 -1, 1, 2, 7, 14, 31, 62, 127, 254, 511, 1022, 2047, 4094, 8191, 16382, 32767, 65534, 131071, 262142, 524287, 1048574, 2097151, 4194302, 8388607, 16777214, 33554431, 67108862, 134217727, 268435454, 536870911 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The inverse binomial transform is 1, 1, 4, -2, 10, -14, 34, -62 which leads to (-1)^(n+1)*A135440(n). For n > 0: A266161(a(n)) = n and A266161(m) < n for m < a(n). - Reinhard Zumkeller, Dec 22 2015 Also, the decimal representation of the diagonal from the corner to the origin 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 Reinhard Zumkeller, 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 FORMULA a(2*n) = 2*A083420(n-1) and a(2*n+1) = A083420(n) a(n+1) - a(n) = A014551(n); Jacobsthal-Lucas numbers. a(2*n) + a(2*n+1) = 9*A002450(n) a(n+1) - 2*a(n) = A010674(n+1); repeat 3, 0. a(n) + A000034(n+1) = A000079(n); powers of 2. a(n)= a(n-1) + 2*a(n-2) + 3. - Gary Detlefs, Jun 22 2010 a(n+1) = A000069(2^n); odious numbers. - Johannes W. Meijer, Jun 24 2011 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>2, a(0) = -1, a(1) = 1, a(2) = 2. - Philippe Deléham, Feb 25 2012 G.f.: (x^2+3*x-1)/((1-2*x)*(1-x)*(1+x)). - Philippe Deléham, Feb 25 2012 MAPLE A140253:=proc(n): if type(n, odd) then 2*4^(((n+1)/2)-1)-1 else 2*(2*4^((n/2)-1)-1) fi: end: seq(A140253(n), n=0..29); # Johannes W. Meijer, Jun 24 2011 MATHEMATICA Table[(2^(n+1) - 3 + (-1)^(n+1))/2, {n, 0, 30}] (* Jean-François Alcover, Jun 05 2017 *) PROG (Haskell) import Data.List (transpose) a140253 n = a140253_list !! n a140253_list = -1 : concat                     (transpose [a083420_list, map (* 2) a083420_list]) -- Reinhard Zumkeller, Dec 22 2015 CROSSREFS Cf. A000034, A000069, A000079, A002450, A010674, A014551, A083420, A266161. Sequence in context: A224916 A258321 A034791 * A018453 A286829 A286861 Adjacent sequences:  A140250 A140251 A140252 * A140254 A140255 A140256 KEYWORD sign,easy AUTHOR Paul Curtz, Jun 23 2008 EXTENSIONS Edited, corrected and information added by Johannes W. Meijer, Jun 24 2011 STATUS approved

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Last modified August 20 05:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)