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A260033 Number of configurations of the general monomer-dimer model for a 2 X 2n square lattice.

%I A260033 #23 Sep 08 2022 08:46:13
%S A260033 1,7,71,733,7573,78243,808395,8352217,86293865,891575391,9211624463,
%T A260033 95173135221,983314691581,10159461285307,104966044432531,
%U A260033 1084493574452273,11204826469232593,115766602184825143,1196083332322900695,12357755266727364237,127678491209925526885
%N A260033 Number of configurations of the general monomer-dimer model for a 2 X 2n square lattice.
%H A260033 Alois P. Heinz, <a href="/A260033/b260033.txt">Table of n, a(n) for n = 0..1000</a>
%H A260033 N. Allegra, <a href="http://arxiv.org/abs/1410.4131">Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics</a>, arXiv:1410.4131 [cond-mat.stat-mech], 2014. See Table 5.
%H A260033 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-7,1).
%F A260033 G.f.: (1-4*x+x^2)/(1-11*x+7*x^2-x^3). - _Alois P. Heinz_, Mar 07 2016
%p A260033 seq(coeff(series((1-4*x+x^2)/(1-11*x+7*x^2-x^3), x, n+1), x, n), n = 0 .. 30); # _G. C. Greubel_, Oct 27 2019
%t A260033 LinearRecurrence[{11,-7,1}, {1,7,71}, 30] (* _G. C. Greubel_, Oct 27 2019 *)
%o A260033 (PARI) my(x='x+O('x^30)); Vec((1-4*x+x^2)/(1-11*x+7*x^2-x^3)) \\ _G. C. Greubel_, Oct 27 2019
%o A260033 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-4*x+x^2)/(1-11*x+7*x^2-x^3) )); // _G. C. Greubel_, Oct 27 2019
%o A260033 (Sage)
%o A260033 def A260033_list(prec):
%o A260033     P.<x> = PowerSeriesRing(ZZ, prec)
%o A260033     return P((1-4*x+x^2)/(1-11*x+7*x^2-x^3)).list()
%o A260033 A260033_list(30) # _G. C. Greubel_, Oct 27 2019
%o A260033 (GAP) a:=[1,7,71];; for n in [4..30] do a[n]:=11*a[n-1]-7*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Oct 27 2019
%Y A260033 Bisection (even part) of A030186.
%K A260033 nonn,easy
%O A260033 0,2
%A A260033 _N. J. A. Sloane_, Jul 19 2015
%E A260033 a(0), a(5)-a(20) from _Alois P. Heinz_, Mar 07 2016