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A287425
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Number of maximal matchings in the n-gear graph.
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2
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3, 6, 11, 22, 47, 98, 198, 394, 776, 1512, 2917, 5582, 10610, 20050, 37697, 70562, 131565, 244460, 452829, 836482, 1541318, 2833624, 5198692, 9519722, 17402027, 31759964, 57878498, 105331522, 191445503, 347548382, 630235055, 1141662370, 2066086475
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OFFSET
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1,1
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COMMENTS
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Extended to a(1)-a(2) using the formula/recurrence.
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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FORMULA
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G.f.: x*(3 - 9*x + 11*x^2 - 9*x^3 + 8*x^4 - 4*x^5 + 2*x^6) / ((1 - x)*(1 - 2*x + x^2 - x^3)^2)). - Colin Barker, May 25 2017
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MATHEMATICA
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LinearRecurrence[{5, -10, 12, -11, 7, -3, 1}, {3, 6, 11, 22, 47, 98, 198}, 30]
CoefficientList[Series[(-3 + 9 x - 11 x^2 + 9 x^3 - 8 x^4 + 4 x^5 - 2 x^6)/((-1 + x) (-1 + 2 x - x^2 + x^3)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 30 2017 *)
Table[2 - n RootSum[-1 + # - 2 #^2 + #^3 &, 6 #^(n + 1) - 11 #^(n + 2) + 2 #^(n + 3) &]/23, {n, 20}] (* Eric W. Weisstein, Dec 30 2017 *)
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PROG
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(PARI) Vec(x*(3 - 9*x + 11*x^2 - 9*x^3 + 8*x^4 - 4*x^5 + 2*x^6) / ((1 - x)*(1 - 2*x + x^2 - x^3)^2) + O(x^40)) \\ Colin Barker, May 25 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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