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A356200
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Number of edge covers in the n-gear graph.
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0
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3, 25, 162, 969, 5613, 32062, 181989, 1030017, 5821902, 32886505, 185714829, 1048619646, 5920559661, 33426829321, 188721717102, 1065481514817, 6015458406741, 33961820796094, 191740095366885, 1082517159435249, 6111623364952302, 34504707439240921
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OFFSET
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1,1
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COMMENTS
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Sequence extended to a(1) using the formula/recurrence.
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LINKS
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FORMULA
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a(n) = (3-sqrt(7))^n + (sqrt(7)+3)^n - Lucas(2*n).
a(n) = 9*a(n-1) - 21*a(n-2) + 12*a(n-3) - 2*a(n-4).
G.f.: x*(3-2*x)/((1-3*x+x^2)*(1-6*x+2*x^2)).
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MATHEMATICA
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Table[(3 - Sqrt[7])^n + (3 + Sqrt[7])^n - LucasL[2 n], {n, 30}] // Expand
CoefficientList[Series[(3 - 2 x)/((1 - 3 x + x^2) (1 - 6 x + 2 x^2)), {x, 0, 20}], x]
LinearRecurrence[{9, -21, 12, -2}, {3, 25, 162, 969}, 20]
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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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STATUS
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approved
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