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A087206 a(n) = 2*a(n-1) + 4*a(n-2); with a(0)=1, a(1)=4.

%I A087206 #42 Jun 07 2025 00:11:43
%S A087206 1,4,12,40,128,416,1344,4352,14080,45568,147456,477184,1544192,
%T A087206 4997120,16171008,52330496,169345024,548012032,1773404160,5738856448,
%U A087206 18571329536,60098084864,194481487872,629355315200,2036636581888
%N A087206 a(n) = 2*a(n-1) + 4*a(n-2); with a(0)=1, a(1)=4.
%C A087206 Binomial transform of A056487. Unsigned version of A152174.
%C A087206 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
%C A087206 From _Sean A. Irvine_, Jun 06 2025: (Start)
%C A087206 Also, the number of walks of length n starting at 0 in the following graph:
%C A087206   1---2
%C A087206   |\ /|
%C A087206   | 0 |
%C A087206   |/ \|
%C A087206   4---3. (End)
%H A087206 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 A087206 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A087206 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 A087206 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,4).
%F A087206 G.f.: (1+2x)/(1-2x-4x^2).
%F A087206 a(n) = (1-sqrt(5))^n*(1/2-3*sqrt(5)/10)+(1+sqrt(5))^n*(1/2+3*sqrt(5)/10).
%F A087206 a(n) = 2^n*Fibonacci(n+2). - _Paul Barry_, Mar 22 2004
%F A087206 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 A087206 G.f.: 1/(-2x-1/(-2x-1)). - _Paul Barry_, Mar 24 2010
%t A087206 LinearRecurrence[{2, 4}, {1, 4}, 25] (* _Jean-François Alcover_, Sep 21 2017 *)
%Y A087206 Cf. A060925, A063782, A253064.
%Y A087206 Equals (1/2) * A063727(n-1). Cf. A006483.
%K A087206 easy,nonn
%O A087206 0,2
%A A087206 _Paul Barry_, Aug 25 2003
%E A087206 Comment corrected by _Philippe Deléham_, Nov 27 2008