A260035 Number of configurations of the general monomer-dimer model for a 6 X 2n square lattice.

1, 733, 1453535, 2989126727, 6158217253688, 12688781322524383, 26145024935911561519, 53871436268769248658909, 111001303100987323499885497, 228716555771886318320544971113, 471267106301726996713836945644741, 971038955798168144904320530113062251

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

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.

Formula

G.f.: -(x^35 -303*x^34+39755*x^33 -3006461*x^32 +147285464*x^31 -4982358541*x^30 +121168594147*x^29 -2178142852763*x^28 +29534187084401*x^27 -306739443130567*x^26 +2469166583241357*x^25 -15545255469711489*x^24 +77061970912745851*x^23 -302229162090568272*x^22 +940552356911616655*x^21 -2325983946004629825*x^20

+4571403782595656681*x^19 -7132536146049218835*x^18 +8816072203220095307*x^17 -8606516438041706909*x^16 +6610116709200270017*x^15 -3975093141652598239*x^14 +1860979721719230536*x^13 -673557512542825639*x^12 +186891256173184345*x^11 -39350096931810689*x^10 +6209590348296227*x^9 -723408237698629*x^8 +61058311803007*x^7 -3643308415243*x^6 +148512309793*x^5 -3929296848*x^4 +62206053*x^3 -513531*x^2 +1715*x -1)

/ (x^36 -340*x^35 +50100*x^34 -4250888*x^33 +233265592*x^32 -8826992892*x^31 +239952846936*x^30 -4819931077916*x^29 +73017958649024*x^28 -847099637555764*x^27 +7614471159726924*x^26 -53515045097001676*x^25 +296113838422354424*x^24 -1296679648512973880*x^23 +4509879534593338500*x^22 -12485812982425137512*x^21 +27542748242886644836*x^20

-48402911844123030224*x^19 +67688232598462447078*x^18 -75169948051576380124*x^17 +66100365055592753276*x^16 -45850942528892434584*x^15 +24969271989493514952*x^14 -10611960050772759700*x^13 +3493906512883743112*x^12 -883034757728796084*x^11 +169388231771649952*x^10 -24321058986990516*x^9 +2569465539974116*x^8 -195540203433060*x^7 +10431777819048*x^6 -376109557320*x^5 +8698993676*x^4 -119339640*x^3 +854380*x^2 -2448*x+1). - Alois P. Heinz, Mar 07 2016

Crossrefs

Bisection (even part) of A033509.

Sequence in context: A346024 A297761 A220625 * A033529 A118055 A025356

Adjacent sequences: A260032 A260033 A260034 * A260036 A260037 A260038

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 19 2015

Extensions

More terms from Alois P. Heinz, Mar 07 2016

Status

approved