%I A137726
%S A137726 2,2,8,9,12,16,23,29,41,56,79,110,158,225,325,469,682,991,1446,2110,3085,
               4511,6603,9666,
%T A137726 14157,20736,30380,44511,65223,95575,140060,205253,300800,440828,646051,
               946817,
%U A137726 1387613,2033628,2980411,4367986,6401578,9381949,13749897,20151433,29533342
%N A137726 Number of sequences of length n with elements {-2,-1,+1,+2}, counted 
               up to simultaneous reversal and negation, such that the sum of elements 
               of the whole sequence but of no proper subsequence equals 0 modulo 
               n. For n>=4, the number of Hamiltonian (undirected) cycles on the 
               circulant graph C_n(1,2).
%C A137726 For n>1, the number of circular permutations (counted up to rotations 
               and reversals) of {0, 1,...,n-1} such that the distance between every 
               two adjacent elements is -2,-1,1,or 2 modulo n.
%H A137726 Mordecai J. Golin and Yiu Cho Leung, <a href="http://www.cse.ust.hk/tcsc/
               RR/2004-02.ps.gz">Unhooking Circulant Graphs: A Combinatorial Method 
               for Counting Spanning Trees, Hamiltonian Cycles and other Parameters</
               a>. Technical report HKUST-TCSC-2004-02.
%H A137726 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CirculantGraph.html">Circulant Graph</a>
%F A137726 For even n>=4, a(n) = n + 3*A000930(n) - 2*A000930(n); for odd n>=3, 
               a(n) = n + 3*A000930(n) - 2*A000930(n)+1.
%F A137726 For n>8, a(n) = 2*a(n-1) - a(n-3) - a(n-5) + a(n-6) or a(n) = a(n-1) 
               + a(n-2) - a(n-5) - 2.
%F A137726 a(n) = A137725(n) / 2.
%Y A137726 Cf. A069241, A124353, A137725
%Y A137726 Sequence in context: A000023 A010584 A131659 this_sequence A121098 A121094 
               A029595
%Y A137726 Adjacent sequences: A137723 A137724 A137725 this_sequence A137727 A137728 
               A137729
%K A137726 nonn
%O A137726 1,1
%A A137726 Max Alekseyev (maxale(AT)gmail.com), Feb 8, 2008