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A028480
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Number of perfect matchings in graph C_{9} X P_{2n}.
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3
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1, 76, 11989, 2091817, 372713728, 66750320449, 11970180565381, 2147314732677364, 385238046548443177, 69115057977256578649, 12399917664600455876068, 2224670061782262303745381, 399128369515444836686385361, 71607684753022827432994707712
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OFFSET
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0,2
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REFERENCES
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Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
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LINKS
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FORMULA
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G.f.: (x^15 -189*x^14+9585*x^13 -194987*x^12 +1937034*x^11 -10357902*x^10 +31195513*x^9 -53951967*x^8 +53951967*x^7 -31195513*x^6 +10357902*x^5 -1937034*x^4 +194987*x^3 -9585*x^2 +189*x -1) / ( -x^16 +265*x^15 -17736*x^14 +457655*x^13 -5699687*x^12 +38357160*x^11 -146975161*x^10 +327381265*x^9 -427427424*x^8 +327381265*x^7 -146975161*x^6 +38357160*x^5 -5699687*x^4 +457655*x^3 -17736*x^2 +265*x -1). - Alois P. Heinz, Dec 10 2013
a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{9}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - Seiichi Manyama, Apr 17 2020
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PROG
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(PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(9, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020
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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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