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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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4
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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
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OFFSET
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1,1
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COMMENTS
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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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FORMULA
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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.
G.f.: -x*(x^7+2*x^5-4*x^4-5*x^3+4*x^2-2*x+2)/((x-1)^2*(x+1)*(x^3+x-1)). - Colin Barker, Aug 22 2012
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MATHEMATICA
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Rest[CoefficientList[Series[-x*(x^7 + 2*x^5 - 4*x^4 - 5*x^3 + 4*x^2 - 2*x + 2)/((x - 1)^2*(x + 1)*(x^3 + x - 1)), {x, 0, 50}], x]] (* G. C. Greubel, Apr 27 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec(-x*(x^7 + 2*x^5 - 4*x^4 - 5*x^3 + 4*x^2 - 2*x + 2)/((x - 1)^2*(x + 1)*(x^3 + x - 1))) \\ G. C. Greubel, Apr 27 2017
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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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