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 A087206 a(n) = 2*a(n-1) + 4*a(n-2); with a(0)=1, a(1)=4. 8
 1, 4, 12, 40, 128, 416, 1344, 4352, 14080, 45568, 147456, 477184, 1544192, 4997120, 16171008, 52330496, 169345024, 548012032, 1773404160, 5738856448, 18571329536, 60098084864, 194481487872, 629355315200, 2036636581888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A056487. Unsigned version of A152174. Number of words of length n over the alphabet {1,2,3,4} such that no odd letter is followed by an odd letter. - Armend Shabani, Feb 18 2017 LINKS Jens Christian Claussen, Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration, arXiv:math/0410429 [math.CO], 2004. See Table II, p. 4. N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015. Index entries for linear recurrences with constant coefficients, signature (2,4). FORMULA G.f.: (1+2x)/(1-2x-4x^2). a(n) = (1-sqrt(5))^n*(1/2-3*sqrt(5)/10)+(1+sqrt(5))^n*(1/2+3*sqrt(5)/10). a(n) = 2^n*Fibonacci(n+2). - Paul Barry, Mar 22 2004 a(n) = ((1+sqrt(5))^n-(1-sqrt(5))^n)/sqrt(80). Offset 2. a(4)=12. - Al Hakanson (hawkuu(AT)gmail.com), Apr 11 2009 G.f.: 1/(-2x-1/(-2x-1)). - Paul Barry, Mar 24 2010 MATHEMATICA LinearRecurrence[{2, 4}, {1, 4}, 25] (* Jean-François Alcover, Sep 21 2017 *) CROSSREFS Cf. A060925, A253064. Equals (1/2) * A063727(n-1). Cf. A006483. Sequence in context: A341990 A090576 A152174 * A275863 A289653 A081875 Adjacent sequences: A087203 A087204 A087205 * A087207 A087208 A087209 KEYWORD easy,nonn AUTHOR Paul Barry, Aug 25 2003 EXTENSIONS Comment corrected by Philippe Deléham, Nov 27 2008 STATUS approved

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Last modified January 28 12:46 EST 2023. Contains 359892 sequences. (Running on oeis4.)