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A127682
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Number of non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets of the n-cycle graph having at least one symmetry axis. Also: Number of cyclic and palindromic compositions of n in which each term is either 2 or 3.
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6
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0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 5, 4, 7, 5, 9, 7, 12, 9, 16, 12, 21, 16, 28, 21, 37, 28, 49, 37, 65, 49, 86, 65, 114, 86, 151, 114, 200, 151, 265, 200, 351, 265, 465, 351, 616, 465, 816, 616, 1081, 816, 1432, 1081, 1897, 1432, 2513, 1897, 3329, 2513, 4410, 3329
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = a(n-4) + a(n-6).
G.f.: -x^2*(x^4+x^3+x^2+x+1) / (x^6+x^4-1). - Colin Barker, Mar 29 2014
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MATHEMATICA
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Rest[CoefficientList[Series[-x^2*(x^4+x^3+x^2+x+1)/(x^6+x^4-1), {x, 0, 63}], x]] (* Vaclav Kotesovec, Mar 29 2014 *)
LinearRecurrence[{0, 0, 0, 1, 0, 1}, {0, 1, 1, 1, 1, 2}, 70] (* Harvey P. Dale, Jul 17 2014 *)
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PROG
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(PARI) concat(0, Vec(-x^2*(x^4+x^3+x^2+x+1)/(x^6+x^4-1) + O(x^100))) \\ Colin Barker, Mar 29 2014
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007
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STATUS
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approved
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