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%I #39 Sep 21 2017 11:00:27
%S 1,4,12,40,128,416,1344,4352,14080,45568,147456,477184,1544192,
%T 4997120,16171008,52330496,169345024,548012032,1773404160,5738856448,
%U 18571329536,60098084864,194481487872,629355315200,2036636581888
%N a(n) = 2*a(n-1) + 4*a(n-2); with a(0)=1, a(1)=4.
%C Binomial transform of A056487. Unsigned version of A152174.
%C 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
%H Jens Christian Claussen, <a href="https://arxiv.org/abs/math/0410429">Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration</a>, arXiv:math/0410429 [math.CO], 2004. See Table II, p. 4.
%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,4).
%F G.f.: (1+2x)/(1-2x-4x^2).
%F a(n) = (1-sqrt(5))^n*(1/2-3*sqrt(5)/10)+(1+sqrt(5))^n*(1/2+3*sqrt(5)/10).
%F a(n) = 2^n*Fibonacci(n+2). - _Paul Barry_, Mar 22 2004
%F 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
%F G.f.: 1/(-2x-1/(-2x-1)). - _Paul Barry_, Mar 24 2010
%t LinearRecurrence[{2, 4}, {1, 4}, 25] (* _Jean-François Alcover_, Sep 21 2017 *)
%Y Cf. A060925, A253064.
%Y Equals (1/2) * A063727(n-1). Cf. A006483.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 25 2003
%E Comment corrected by _Philippe Deléham_, Nov 27 2008
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