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%I #28 Sep 08 2022 08:44:51
%S 1,7,108,1511,21497,305184,4334009,61545775,873996300,12411393231,
%T 176250978417,2502894414208,35542954271729,504736272807255,
%U 7167628868280044,101785638086283959,1445431440583263081,20526196904667164704,291487197206091205801
%N Number of matchings in graph C_{4} X P_{n}.
%D 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.
%H Alois P. Heinz, <a href="/A033516/b033516.txt">Table of n, a(n) for n = 0..800</a>
%H J. L. Hock, R. B. McQuistan< <a href="http://dx.doi.org/10.1063/1.525908">The occupation statistics for indistinguishable dumbbells on a 2X2XN lattice space</a>, J. Math. Phys 24 (7) (1983) 1859, Table 1.
%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (14,6,-46,18,2,-1).
%F G.f.: -(x^4 -3*x^3 -4*x^2 +7*x -1) / (x^6 -2*x^5 -18*x^4 +46*x^3 -6*x^2 -14*x +1). - _Alois P. Heinz_, Dec 09 2013
%p seq(coeff(series((1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4 -2*x^5+x^6), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Oct 26 2019
%t LinearRecurrence[{14,6,-46,18,2,-1}, {1,7,108,1511,21497,305184}, 30] (* _G. C. Greubel_, Oct 26 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2 +46*x^3-18*x^4-2*x^5+x^6)) \\ _G. C. Greubel_, Oct 26 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4-2*x^5+x^6) )); // _G. C. Greubel_, Oct 26 2019
%o (Sage)
%o def A033516_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-7*x+4*x^2+3*x^3-x^4)/(1-14*x-6*x^2+46*x^3-18*x^4-2*x^5 +x^6) ).list()
%o A033516_list(30) # _G. C. Greubel_, Oct 26 2019
%o (GAP) a:=[1,7,108,1511,21497,305184];; for n in [4..30] do a[n]:=14*a[n-1]+6*a[n-2]-46*a[n-3]+18*a[n-4]+2*a[n-5]-a[n-6]; od; a; # _G. C. Greubel_, Oct 26 2019
%Y Row 4 of A287428.
%K nonn,easy
%O 0,2
%A _Per H. Lundow_
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