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A288038
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Number of independent vertex sets in the n-Andrásfai graph.
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1
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3, 11, 33, 89, 225, 545, 1281, 2945, 6657, 14849, 32769, 71681, 155649, 335873, 720897, 1540097, 3276801, 6946817, 14680065, 30932993, 65011713, 136314881, 285212673, 595591169, 1241513985, 2583691265, 5368709121, 11140071425, 23085449217, 47781511169
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OFFSET
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1,1
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COMMENTS
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The independence polynomial is given by I(n,x) = 1+(3*n-1)*x*(x+1)^(n-1).
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LINKS
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FORMULA
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a(n) = 1 + (3*n-1)*2^(n-1).
G.f.: x*(3 - 4*x + 2*x^2) / ((1 - x)*(1 - 2*x)^2).
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>3.
(End)
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MATHEMATICA
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Table[(3 n - 1) 2^(n - 1) + 1, {n, 20}]
LinearRecurrence[{5, -8, 4}, {3, 11, 33}, 20]
CoefficientList[Series[(-3 + 4 x - 2 x^2)/((-1 + x) (-1 + 2 x)^2), {x, 0, 20}], x]
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PROG
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(PARI) Vec(x*(3 - 4*x + 2*x^2) / ((1 - x)*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Jun 05 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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