cp's OEIS Frontend

A038758 Number of ways of covering a 2n X 2n lattice by 2n^2 dominoes with exactly 4 horizontal (or vertical) dominoes.

%I A038758 #26 Jul 02 2025 16:01:56
%S A038758 16,281,1785,7175,22015,56406,126966,259170,490050,871255,1472471,
%T A038758 2385201,3726905,5645500,8324220,11986836,16903236,23395365,31843525,
%U A038758 42693035,56461251,73744946,95228050,121689750,154012950,193193091
%N A038758 Number of ways of covering a 2n X 2n lattice by 2n^2 dominoes with exactly 4 horizontal (or vertical) dominoes.
%H A038758 Vincenzo Librandi, <a href="/A038758/b038758.txt">Table of n, a(n) for n = 2..1000</a>
%H A038758 M. E. Fisher, <a href="http://dx.doi.org/10.1103/PhysRev.124.1664">Statistical mechanics of dimers on a plane lattice</a>, Physical Review, 124 (1961), 1664-1672.
%H A038758 P. W. Kasteleyn, <a href="http://dx.doi.org/10.1016/0031-8914(61)90063-5">The Statistics of Dimers on a Lattice</a>, Physica, 27 (1961), 1209-1225.
%H A038758 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%H A038758 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A038758 a(n) = (1/24)*n*(n-1)*(n+1)*(12*n^3-11*n-10).
%F A038758 G.f.: x^2*(16+169*x+154*x^2+21*x^3)/(1-x)^7. [_Colin Barker_, Jun 26 2012]
%e A038758 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.
%t A038758 CoefficientList[Series[(16 + 169 x + 154 x^2 + 21 x^3)/(1 - x)^7, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%o A038758 (Magma) [(1/24)*n*(n-1)*(n+1)*(12*n^3-11*n-10): n in [2..30]]; // _Vincenzo Librandi_, Oct 22 2013
%Y A038758 Cf. A004003, A002414, A054344.
%K A038758 nonn,easy
%O A038758 2,1
%A A038758 Yong Kong (ykong(AT)curagen.com), May 06 2000
%E A038758 More terms from _James Sellers_, May 10 2000