OFFSET
0,3
COMMENTS
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
Complete sequence: every positive integer is the sum of members of this sequence. - Charles R Greathouse IV, Jul 19 2012
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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
D. A. Gewurz and F. Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seq., 6 (2003), 03.1.6.
Index entries for linear recurrences with constant coefficients, signature (0,3).
FORMULA
O.g.f.: (1+x)/(1-3*x^2). - R. J. Mathar, Apr 01 2008
a(n) = 3^(n/2)*((1+(-1)^n)/2+(1-(-1)^n)/(2*sqrt(3))). - Paul Barry, Nov 12 2009
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
a(n) = (-1)^n*sum(A158020(n,k)*2^k, 0<=k<=n). - Philippe Deléham, Dec 01 2011
a(n) = sum(A152815(n,k)*2^k, 0<=k<=n). - Philippe Deléham, Apr 22 2013
a(n) = 3^A004526(n). - Michel Marcus, Aug 30 2014
E.g.f.: cosh(sqrt(3)*x) + sinh(sqrt(3)*x)/sqrt(3). - Stefano Spezia, Dec 31 2022
EXAMPLE
a(6) = 27; 3^floor(6/2) = 3^floor(3) = 3^3 = 27.
MAPLE
MATHEMATICA
Table[3^Floor[n/2], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 01 2013 *)
PROG
(PARI) a(n)=3^floor(n/2);
(Magma) [3^Floor(n/2): n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
(Haskell)
a108411 = (3 ^) . flip div 2 -- Reinhard Zumkeller, May 01 2014
(Python)
def A108411(n): return 3**(n>>1) # Chai Wah Wu, Oct 28 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Jun 05 2005
EXTENSIONS
Incorrect formula removed by Michel Marcus, Oct 06 2021
STATUS
approved