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A028478 Number of perfect matchings in graph C_{7} X P_{2n}. 3


%S 1,29,1471,79808,4375897,240378643,13209069847,725898384359,

%T 39891876471539,2192269974717929,120476898663671488,

%U 6620847045486150863,363850801995789860221,19995539171949615541457,1098861359580093467365169,60388283471627147242052029

%N Number of perfect matchings in graph C_{7} X P_{2n}.

%D 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.

%H Alois P. Heinz, <a href="/A028478/b028478.txt">Table of n, a(n) for n = 0..500</a>

%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.

%F G.f.: (x^7 -42*x^6 +364*x^5 -1001*x^4 +1001*x^3 -364*x^2 +42*x -1)/( -x^8 +71*x^7 -952*x^6 +3976*x^5 -6384*x^4 +3976*x^3 -952*x^2 +71*x -1). - _Alois P. Heinz_, Dec 09 2013

%F a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{7}(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

%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(7, 1, I*x/2)))} \\ _Seiichi Manyama_, Apr 17 2020

%K nonn,easy

%O 0,2

%A _Per H. Lundow_

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)