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A054344 Number of ways of covering a 2n X 2n lattice with 2n^2 dominoes of which exactly 6 are horizontal (or vertical) dominoes. 3

%I

%S 9,1064,21656,197484,1143366,4927524,17240292,51631617,137044523,

%T 330284988,735542444,1533609350,3024043008,5684167992,10249533240,

%U 17821214019,30006185613,49097892704,78305096016

%N Number of ways of covering a 2n X 2n lattice with 2n^2 dominoes of which exactly 6 are horizontal (or vertical) dominoes.

%H Vincenzo Librandi, <a href="/A054344/b054344.txt">Table of n, a(n) for n = 2..1000</a>

%H 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 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 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = (1/720)*n*(n+1)*(120*n^7-300*n^6-70*n^5+363*n^4+416*n^3-231*n^2-394*n-264).

%F G.f.: x^2*(x^9-10*x^8+45*x^7-36*x^6+3096*x^5+17256*x^4+27724*x^3+11421*x^2+974*x+9)/(x-1)^10. - _Colin Barker_, Jun 26 2012

%e a(3) = 1064 because we have 1064 ways to cover a 36 X 36 lattice with exactly 6 horizontal (or vertical) dominoes and exactly 12 vertical (or horizontal) dominoes.

%t CoefficientList[Series[(x^9-10*x^8+45*x^7-36*x^6+3096*x^5 +17256*x^4 +27724*x^3+11421*x^2+974*x+9)/(x-1)^10,{x,0,30}],x] (* _Vincenzo Librandi_, Jun 26 2012 *)

%Y Cf. A004003, A002414, A038758.

%K nonn,easy

%O 2,1

%A Yong Kong (ykong(AT)curagen.com), May 06 2000

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)