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A287485
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Number of independent vertex sets and vertex covers in the n-web graph.
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0
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2, 20, 68, 304, 1232, 5168, 21408, 89088, 370112, 1538560, 6394368, 26577664, 110464512, 459127808, 1908282368, 7931445248, 32965660672, 137016012800, 569483091968, 2366956929024, 9837842644992, 40889273090048, 169949115056128, 706363785412608, 2935877583634432, 12202461910794240
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Web Graph
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FORMULA
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G.f.: -2*x*(1 + 8*x + 6*x^2)/(-1 + 2*x + 8*x^2 + 4*x^3).
a(n) = 2*a(n-1) + 8*a(n-2) + 4*a(n-3).
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MATHEMATICA
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Table[RootSum[-4 - 8 # - 2 #^2 + #^3 &, #^n &], {n, 20}]
LinearRecurrence[{2, 8, 4}, {2, 20, 68}, 20]
CoefficientList[Series[-2 (1 + 8 x + 6 x^2)/(-1 + 2 x + 8 x^2 + 4 x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 27 2017 *)
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PROG
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(PARI) Vec(-2*x*(1+8*x+6*x^2)/(-1+2*x+8*x^2+4*x^3) + O(x^30)) \\ Michel Marcus, Sep 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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STATUS
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approved
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