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A108411
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a(n) = 3^floor(n/2). Powers of 3 repeated.
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35
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1, 1, 3, 3, 9, 9, 27, 27, 81, 81, 243, 243, 729, 729, 2187, 2187, 6561, 6561, 19683, 19683, 59049, 59049, 177147, 177147, 531441, 531441, 1594323, 1594323, 4782969, 4782969, 14348907, 14348907, 43046721, 43046721, 129140163, 129140163, 387420489, 387420489, 1162261467
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = 3^(n/2)*((1+(-1)^n)/2+(1-(-1)^n)/(2*sqrt(3))). - Paul Barry, Nov 12 2009
E.g.f.: cosh(sqrt(3)*x) + sinh(sqrt(3)*x)/sqrt(3). - Stefano Spezia, Dec 31 2022
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EXAMPLE
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a(6) = 27; 3^floor(6/2) = 3^floor(3) = 3^3 = 27.
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MAPLE
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MATHEMATICA
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PROG
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(PARI) a(n)=3^floor(n/2);
(Haskell)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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