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A028486
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Number of perfect matchings in graph C_{15} X P_{2n}.
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3
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1, 1364, 6323504, 35269184041, 207171729355756, 1240837214254999769, 7491895591984935317759, 45390122553039546330628096, 275408624219475075609746445361, 1672150595320335623747680596071399, 10155382441518040205071335049138555724
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OFFSET
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0,2
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COMMENTS
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For odd values of m the order of recurrence relation for the number of perfect matchings in C_{m} X P_{2n} graph does not exceed 2^floor(m/2). In general, this estimate is accurate, however the case m = 15 is an exception. This sequence obeys the recurrence relation of order 120. - Sergey Perepechko, Apr 28 2015
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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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a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{15}(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(15, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020
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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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STATUS
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approved
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