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A038758 Number of ways of covering a 2n X 2n lattice by 2n^2 dominoes with exactly 4 horizontal (or vertical) dominoes. 3
16, 281, 1785, 7175, 22015, 56406, 126966, 259170, 490050, 871255, 1472471, 2385201, 3726905, 5645500, 8324220, 11986836, 16903236, 23395365, 31843525, 42693035, 56461251, 73744946, 95228050, 121689750, 154012950, 193193091 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Physical Review, 124 (1961), 1664-1672.
P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.
FORMULA
a(n) = (1/24)*n*(n-1)*(n+1)*(12*n^3-11*n-10).
G.f.: x^2*(16+169*x+154*x^2+21*x^3)/(1-x)^7. [Colin Barker, Jun 26 2012]
EXAMPLE
a(3) = 281 because we have 281 ways to cover a 4 X 4 lattice with exactly 4 horizontal dominoes and exactly 14 vertical dominoes.
MATHEMATICA
CoefficientList[Series[(16 + 169 x + 154 x^2 + 21 x^3)/(1 - x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
PROG
(Magma) [(1/24)*n*(n-1)*(n+1)*(12*n^3-11*n-10): n in [2..30]]; // Vincenzo Librandi, Oct 22 2013
CROSSREFS
Sequence in context: A004382 A204955 A189955 * A240336 A281341 A298284
KEYWORD
nonn,easy
AUTHOR
Yong Kong (ykong(AT)curagen.com), May 06 2000
EXTENSIONS
More terms from James A. Sellers, May 10 2000
STATUS
approved

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Last modified May 19 19:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)