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

0,2

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).

Formula

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

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 *)

Prog

(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
(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
(Sage)
def A260033_list(prec):
    P.<x> = 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
(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

Crossrefs

Bisection (even part) of A030186.

Sequence in context: A100895 A065537 A048552 * A067307 A334135 A357155

Adjacent sequences: A260030 A260031 A260032 * A260034 A260035 A260036

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 19 2015

Extensions

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

Status

approved