|
%I #28 Sep 08 2022 08:44:51
%S 1,11,342,9213,253880,6974078,191668283,5267252351,144751259054,
%T 3977955684680,109319496849249,3004244633718754,82560623863809043,
%U 2268875354470436757,62351701497747569760,1713507386797976483977,47089453761312228669727,1294080593187150583795074
%N Number of matchings in graph C_{5} X P_{n}.
%H Alois P. Heinz, <a href="/A033517/b033517.txt">Table of n, a(n) for n = 0..500</a>
%H 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 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.pdf">Enumeration of matchings in polygraphs</a>, 1998.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (25,76,-209,-159,119,40,-3,-1).
%F G.f.: (1 - 14*x - 9*x^2 + 36*x^3 + 21*x^4 - 2*x^5 - x^6)/(1 - 25*x - 76*x^2 + 209*x^3 + 159*x^4 - 119*x^5 - 40*x^6 + 3*x^7 + x^8). - _Alois P. Heinz_, Dec 09 2013
%p seq(coeff(series((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2 +209*x^3+159*x^4-119*x^5-40*x^6+3*x^7+x^8), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Oct 26 2019
%t LinearRecurrence[{25,76,-209,-159,119,40,-3,-1}, {1,11,342,9213,253880, 6974078,191668283,5267252351}, 30] (* _G. C. Greubel_, Oct 26 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1 -25*x-76*x^2+209*x^3+159*x^4-119*x^5-40*x^6+3*x^7+x^8)) \\ _G. C. Greubel_, Oct 26 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2+209*x^3+159*x^4-119*x^5 -40*x^6+3*x^7+x^8) )); // _G. C. Greubel_, Oct 26 2019
%o (Sage)
%o def A077952_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1-14*x-9*x^2+36*x^3+21*x^4-2*x^5-x^6)/(1-25*x-76*x^2 +209*x^3 +159*x^4-119*x^5-40*x^6+3*x^7+x^8)).list()
%o A077952_list(30) # _G. C. Greubel_, Oct 26 2019
%o (GAP) a:=[1, 11, 342, 9213, 253880, 6974078, 191668283, 5267252351];; for n in [9..30] do a[n]:=25*a[n-1]+76*a[n-2]-209*a[n-3]-159*a[n-4]+119*a[n-5]+40*a[n-6]=3*a[n-7]-a[n-8]; od; a; # _G. C. Greubel_, Oct 26 2019
%Y Row 5 of A287428.
%K nonn,easy
%O 0,2
%A _Per H. Lundow_
|
