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Search: id:A137726
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| A137726 |
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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). |
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+0
3
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| 2, 2, 8, 9, 12, 16, 23, 29, 41, 56, 79, 110, 158, 225, 325, 469, 682, 991, 1446, 2110, 3085, 4511, 6603, 9666, 14157, 20736, 30380, 44511, 65223, 95575, 140060, 205253, 300800, 440828, 646051, 946817, 1387613, 2033628, 2980411, 4367986, 6401578, 9381949, 13749897, 20151433, 29533342
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Mordecai J. Golin and Yiu Cho Leung, Unhooking Circulant Graphs: A Combinatorial Method for Counting Spanning Trees, Hamiltonian Cycles and other Parameters. Technical report HKUST-TCSC-2004-02.
Eric Weisstein's World of Mathematics, Circulant Graph
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FORMULA
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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.
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.
a(n) = A137725(n) / 2.
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CROSSREFS
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Cf. A069241, A124353, A137725
Sequence in context: A000023 A010584 A131659 this_sequence A121098 A121094 A029595
Adjacent sequences: A137723 A137724 A137725 this_sequence A137727 A137728 A137729
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 8, 2008
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