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 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
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