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A287497
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Number of maximal matchings in the n-web graph.
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1
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1, 9, 22, 53, 166, 432, 1212, 3341, 9175, 25364, 69829, 192560, 530830, 1463170, 4033687, 11119101, 30651528, 84495213, 232922084, 642082488, 1769987094, 4879211973, 13450215173, 37077354584, 102208799091, 281752521488, 776689338352, 2141050324382
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OFFSET
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1,2
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COMMENTS
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Extended to a(1)-a(2) using the formula.
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LINKS
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Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Web Graph
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FORMULA
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a(n) = a(n-1)+4*a(n-2)+3*a(n-3)-2*a(n-4)+a(n-6).
G.f.: (x*(-1-8*x-9*x^2+8*x^3-6*x^5))/(-1+x+4*x^2+3*x^3-2*x^4+x^6).
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MATHEMATICA
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LinearRecurrence[{1, 4, 3, -2, 0, 1}, {1, 9, 22, 53, 166, 432}, 20]
Rest @ CoefficientList[Series[(x (-1 - 8 x - 9 x^2 + 8 x^3 - 6 x^5))/(-1 + x + 4 x^2 + 3 x^3 - 2 x^4 + x^6), {x, 0, 20}], x]
Table[RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^n &], {n, 20}]
RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^Range[20] &] (* Eric W. Weisstein, Dec 30 2017 *)
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PROG
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(Magma) I:=[1, 9, 22, 53, 166, 432]; [n le 6 select I[n] else Self(n-1)+4*Self(n-2)+3*Self(n-3)-2*Self(n-4)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Sep 03 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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