A260034 Number of configurations of the general monomer-dimer model for a 4 X 2n square lattice.

1, 71, 10012, 1453535, 211351945, 30734932553, 4469527322891, 649966808093412, 94519361817920403, 13745178487929574337, 1998848998552669987841, 290676277692731170734063, 42270676011348793634137996, 6147079027705968859829472231, 893919476535411566264300633833

Offset: 0

Author

N. J. A. Sloane, Jul 19 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..460
• 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 (163, -2641, 12479, -22577, 16705, -5331, 769, -47, 1).

Crossrefs

Bisection (even part) of A033507.

Programs

Mathematica

LinearRecurrence[{163, -2641, 12479, -22577, 16705, -5331, 769, -47, 1}, {1, 71, 10012, 1453535, 211351945, 30734932553, 4469527322891, 649966808093412, 94519361817920403}, 20] (* Jean-François Alcover, Dec 15 2018 *)

Formula

G.f.: -(x^8 -36*x^7 +432*x^6 -2033*x^5 +4000*x^4 -3389*x^3 +1080*x^2 -92*x +1) / (x^9 -47*x^8 +769*x^7 -5331*x^6 +16705*x^5 -22577*x^4 +12479*x^3 -2641*x^2 +163*x -1). - Alois P. Heinz, Mar 07 2016

Extensions

a(0), a(5)-a(14) from Alois P. Heinz, Mar 07 2016