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A192857
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Number of matchings in the n-web graph.
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1
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4, 3, 23, 93, 439, 1988, 9107, 41583, 190047, 868341, 3967828, 18130335, 82844095, 378544117, 1729703523, 7903633148, 36114524127, 165020163823, 754036089983, 3445460307689, 15743539192644, 71937855657915, 328709765539959, 1501992365110237, 6863139770575695, 31360137777380788
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OFFSET
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0,1
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COMMENTS
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Extended to a(0)-a(2) using the recurrence.
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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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G.f.: (1+x)*(4 - 13*x - x^2)/(1 - 3*x - 7*x^2 - x^3 + x^4).
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MATHEMATICA
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LinearRecurrence[{3, 7, 1, -1}, {4, 3, 23, 93, 439}, 30] (* Eric W. Weisstein, Mar 09 2016; amended for a(0) by Georg Fischer, Apr 03 2019 *)
RootSum[1 - # - 7 #^2 - 3 #^3 + #^4 &, #^Range[0, 30] &] (* Eric W. Weisstein, Oct 03 2017 *)
CoefficientList[Series[(4-9x-14x^2-x^3)/(1-3x-7x^2-x^3+x^4), {x, 0, 30}], x] (* Eric W. Weisstein, Oct 03 2017 *)
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PROG
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(PARI) polsym(x^4 - 3*x^3 - 7*x^2 - x + 1, 30) \\ Joerg Arndt, May 26 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4) )); // G. C. Greubel, Jan 06 2019
(Sage) ((1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 06 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Redefined to include all web graphs, a(9)-a(25) from Andrew Howroyd, Mar 08 2016
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STATUS
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approved
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