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A033506
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Number of matchings in graph P_{3} X P_{n}.
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4
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1, 3, 22, 131, 823, 5096, 31687, 196785, 1222550, 7594361, 47177097, 293066688, 1820552297, 11309395995, 70254767718, 436427542283, 2711118571311, 16841658983944, 104621568809247, 649916534985369, 4037327172325542
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OFFSET
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0,2
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REFERENCES
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Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 50, 999.
Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research reports, No 12, 1996, Department of Mathematics, Umea University.
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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.: (1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2+9*x^3+x^4-x^5)). - Sergey Perepechko, Apr 19 2013
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MAPLE
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seq(coeff(series((1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2+9*x^3+x^4-x^5 )), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 26 2019
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MATHEMATICA
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CoefficientList[Series[(1-2x-x^2)(1+x-x^2)/((1+x)(1-5x-9x^2+9x^3+x^4-x^5) ), {x, 0, 30}], x] (* Harvey P. Dale, Dec 05 2014 *)
LinearRecurrence[{4, 14, 0, -10, 0, 1}, {1, 3, 22, 131, 823, 5096}, 30] (* Harvey P. Dale, Dec 05 2014 *)
Table[RootSum[-1 +# +9#^2 -9#^3 -5#^4 +#^5 &, 1436541#^n + 3941068#^(n+1) -6086452#^(n+2) -2800519#^(n+3) +591744#^(n+4) &]/10204570 -(-1)^n/5, {n, 20}] (* Eric W. Weisstein, Oct 02 2017 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2 +9*x^3+x^4-x^5))) \\ G. C. Greubel, Oct 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2+9*x^3+x^4-x^5)) )); // G. C. Greubel, Oct 26 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-2*x-x^2)*(1+x-x^2)/((1+x)*(1-5*x-9*x^2+9*x^3+x^4-x^5)) ).list()
(GAP) a:=[1, 3, 22, 131, 823, 5096];; for n in [7..30] do a[n]:=4*a[n-1] +14*a[n-2]-10*a[n-4]+a[n-6]; od; a; # G. C. Greubel, Oct 26 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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STATUS
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approved
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