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

1, 7, 71, 733, 7573, 78243, 808395, 8352217, 86293865, 891575391, 9211624463, 95173135221, 983314691581, 10159461285307, 104966044432531, 1084493574452273, 11204826469232593, 115766602184825143, 1196083332322900695, 12357755266727364237, 127678491209925526885

Offset: 0

Author

N. J. A. Sloane, Jul 19 2015

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. Allegra, Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics, arXiv:1410.4131 [cond-mat.stat-mech], 2014. See Table 5.
• Index entries for linear recurrences with constant coefficients, signature (11,-7,1).

Crossrefs

Bisection (even part) of A030186.

Programs

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

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-4*x+x^2)/(1-11*x+7*x^2-x^3) )); // G. C. Greubel, Oct 27 2019

Maple

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

Mathematica

LinearRecurrence[{11,-7,1}, {1,7,71}, 30] (* G. C. Greubel, Oct 27 2019 *)

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

Sage

def A260033_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1-4*x+x^2)/(1-11*x+7*x^2-x^3)).list()
A260033_list(30) # G. C. Greubel, Oct 27 2019

Formula

G.f.: (1-4*x+x^2)/(1-11*x+7*x^2-x^3). - Alois P. Heinz, Mar 07 2016

Extensions

a(0), a(5)-a(20) from Alois P. Heinz, Mar 07 2016