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A347054
Number of domino tilings of a 32 X n rectangle.
0
1, 1, 3524578, 1117014753, 170220478472105, 224916047725262248, 12348080425980866090537, 30648981125778378496845537, 1010618564986361239515088848178, 3596059736380751648485086101179655, 87171995375835553001398855677616476448, 391978133958466896956216157693001644153072
OFFSET
0,3
COMMENTS
It is known that the number of domino tilings of an m X n rectangle is equal to the number of perfect matchings in the m X n grid graph.
REFERENCES
A. M. Magomedov, T. A. Magomedov, S. A. Lawrencenko, Mutually-recursive formulas for enumerating partitions of the rectangle, [in Russian, English summary], Prikl. Diskretn. Mat., 46 (2019), 108-121. DOI: 10.17223/20710410/46/9
A. M. Magomedov and S. A. Lavrenchenko, Computational aspects of the partition enumeration problem, [in Russian, English summary], Dagestan Electronic Mathematical Reports, 14 (2020), 1-21. DOI: 10.31029/demr.14.1
LINKS
M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev., 124 (1961), 1664-1672.
P. W. Kasteleyn, Dimer statistics and phase transitions, J. Math. Phys., 4 (1963), 287-293.
V.-H. Nguyen, K. Perrot, M. Vallet, NP-completeness of the game Kingdomino{TM}, Theoret. Comput. Sci., 822 (2020), 23-35.
FORMULA
a(n) = Product_{j=1..16} (Product_{k=1..floor(n/2)}(4*(cos(j*Pi/33))^2+ 4*(cos(k*Pi/(n+1)))^2)) (special case of the double product formula in A099390).
MATHEMATICA
Do[ P=1;
Do[P=P*4*(Cos[Pi*i/(n+1)]^2+Cos[Pi*j/33]^2), {i, 1, n/2}, {j, 1, 16}];
Print["n=", n , ":", Round[P]], {n, 1, 11000}]
CROSSREFS
Column n=32 of A187596.
Sequence in context: A237006 A209785 A244620 * A202570 A348809 A209857
KEYWORD
nonn
AUTHOR
A. M. Magomedov and Serge Lawrencenko, Aug 14 2021
STATUS
approved