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A108411 a(n) = 3^floor(n/2). Powers of 3 repeated.

%I A108411 #85 May 31 2025 10:29:08
%S A108411 1,1,3,3,9,9,27,27,81,81,243,243,729,729,2187,2187,6561,6561,19683,
%T A108411 19683,59049,59049,177147,177147,531441,531441,1594323,1594323,
%U A108411 4782969,4782969,14348907,14348907,43046721,43046721,129140163,129140163,387420489,387420489,1162261467
%N A108411 a(n) = 3^floor(n/2). Powers of 3 repeated.
%C A108411 a(n) is the Parker sequence for the automorphism group of the limit of the class of oriented graphs; a(n) counts the finite circulant structures in that class. - _N-E. Fahssi_, Feb 18 2008
%C A108411 Complete sequence: every positive integer is the sum of members of this sequence. - _Charles R Greathouse IV_, Jul 19 2012
%C A108411 Conjecture: a(n+1) is the number of distinct subsets S of {0,1,2,...,n} such that the sumset S+S does not contain n. - _Michael Chu_, Oct 05 2021. _Andrew Howroyd_, Nov 20 2021: The conjecture is true: If there are m pairs of numbers that add to n then inclusion/exclusion gives sum(k=0, m, binomial(m,k)*(-1)^k*2^(2*m-2*k)) as the number of sets that don't contain any of those pairs which equals 3^m. For even n , n/2 cannot be included in any set.
%C A108411 Also, number of walks of length n in the graph K_{1,3} (the graph with edges {1,2}, {1,3}, {1,4}) starting at one of the degree 1 vertices. - _Sean A. Irvine_, May 30 2025
%H A108411 Vincenzo Librandi, <a href="/A108411/b108411.txt">Table of n, a(n) for n = 0..3000</a>
%H A108411 D. A. Gewurz and F. Merola, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seq., 6 (2003), 03.1.6.
%H A108411 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F A108411 O.g.f.: (1+x)/(1-3*x^2). - _R. J. Mathar_, Apr 01 2008
%F A108411 a(n) = 3^(n/2)*((1+(-1)^n)/2+(1-(-1)^n)/(2*sqrt(3))). - _Paul Barry_, Nov 12 2009
%F A108411 a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%F A108411 a(n) = (-1)^n*sum(A158020(n,k)*2^k, 0<=k<=n). - _Philippe Deléham_, Dec 01 2011
%F A108411 a(n) = sum(A152815(n,k)*2^k, 0<=k<=n). - _Philippe Deléham_, Apr 22 2013
%F A108411 a(n) = 3^A004526(n). - _Michel Marcus_, Aug 30 2014
%F A108411 E.g.f.: cosh(sqrt(3)*x) + sinh(sqrt(3)*x)/sqrt(3). - _Stefano Spezia_, Dec 31 2022
%e A108411 a(6) = 27; 3^floor(6/2) = 3^floor(3) = 3^3 = 27.
%p A108411 A108411:=n->3^floor(n/2); seq(A108411(k), k=0..100); # _Wesley Ivan Hurt_, Nov 01 2013
%t A108411 Table[3^Floor[n/2], {n,0,100}] (* _Wesley Ivan Hurt_, Nov 01 2013 *)
%o A108411 (PARI) a(n)=3^floor(n/2);
%o A108411 (Magma) [3^Floor(n/2): n in [0..50]]; // _Vincenzo Librandi_, Aug 17 2011
%o A108411 (Haskell)
%o A108411 a108411 = (3 ^) . flip div 2  -- _Reinhard Zumkeller_, May 01 2014
%o A108411 (Python)
%o A108411 def A108411(n): return 3**(n>>1) # _Chai Wah Wu_, Oct 28 2024
%Y A108411 Essentially the same as A056449 and A162436.
%Y A108411 Cf. A000244, A004526, A016116, A152815, A158020.
%K A108411 nonn,easy
%O A108411 0,3
%A A108411 _Ralf Stephan_, Jun 05 2005
%E A108411 Incorrect formula removed by _Michel Marcus_, Oct 06 2021