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A033515 Number of matchings in graph C_{3} X P_{n}.

%I A033515 #26 Sep 08 2022 08:44:51
%S A033515 1,4,32,228,1655,11978,86731,627960,4546684,32919766,238352021,
%T A033515 1725762060,12495193865,90470101964,655039004548,4742739182904,
%U A033515 34339290944491,248629928211118,1800178148762579,13033995507292632,94371237091674512,683284752187469642
%N A033515 Number of matchings in graph C_{3} X P_{n}.
%H A033515 Alois P. Heinz, <a href="/A033515/b033515.txt">Table of n, a(n) for n = 0..1000</a>
%H A033515 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors.pdf">Computation of matching polynomials and the number of 1-factors in polygraphs</a>, Research reports, No 12, 1996, Department of Mathematics, Umea University.
%H A033515 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.pdf">Enumeration of matchings in polygraphs</a>, 1998.
%H A033515 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,9,0,-1).
%F A033515 G.f.: (1 - 2*x - x^2)/(1 - 6*x - 9*x^2 + x^4). - _Alois P. Heinz_, Dec 09 2013
%p A033515 seq(coeff(series((1-2*x-x^2)/(1-6*x-9*x^2+x^4), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Oct 26 2019
%t A033515 LinearRecurrence[{6,9,0,-1}, {1,4,32,228}, 30] (* _G. C. Greubel_, Oct 26 2019 *)
%o A033515 (PARI) my(x='x+O('x^30)); Vec((1-2*x-x^2)/(1-6*x-9*x^2+x^4)) \\ _G. C. Greubel_, Oct 26 2019
%o A033515 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x-x^2)/(1-6*x-9*x^2+x^4) )); // _G. C. Greubel_, Oct 26 2019
%o A033515 (Sage)
%o A033515 def A033515_list(prec):
%o A033515     P.<x> = PowerSeriesRing(ZZ, prec)
%o A033515     return P((1-2*x-x^2)/(1-6*x-9*x^2+x^4)).list()
%o A033515 A033515_list(30) # _G. C. Greubel_, Oct 26 2019
%o A033515 (GAP) a:=[1,4,32,228];; for n in [5..30] do a[n]:=6*a[n-1]+9*a[n-2]-a[n-4]; od; a; # _G. C. Greubel_, Oct 26 2019
%Y A033515 Row 3 of A287428.
%K A033515 nonn,easy
%O A033515 0,2
%A A033515 _Per H. Lundow_