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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 Vincenzo Librandi, Table of n, a(n) for n = 2..1000 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. Index entries for sequences related to dominoes Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). 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 Cf. A004003, A002414, A054344. Sequence in context: A004382 A204955 A189955 * A240336 A281341 A298284 Adjacent sequences: A038755 A038756 A038757 * A038759 A038760 A038761 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.)