%I A099390
%S A099390 0,1,1,0,2,0,1,3,3,1,0,5,0,5,0,1,8,11,11,8,1,0,13,0,36,0,13,0,1,21,41,
%T A099390 95,95,41,21,1,0,34,0,281,0,281,0,34,0,1,55,153,781,1183,1183,781,153,
%U A099390 55,1,0,89,0,2245,0,6728,0,2245,0,89,0,1,144,571,6336,14824,31529
%N A099390 Array T(m,n) read by antidiagonals: number of domino tilings of the m 
               X n grid.
%H A099390 F. Ardila and R. P. Stanley, <a href="http://arXiv.org/abs/math.CO/0501170">
               Tilings</a>
%H A099390 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A099390 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A099390 P. E. John and H. Sachs, <a href="http://arXiv.org/abs/math.CO/9801094">
               On a strange observation in the theory of the dimer problem</a>
%H A099390 Per Hakan Lundow, <a href="http://abel.math.umu.se/~phl/Text/">Enumeration 
               of matchings in polygraphs</a>, 1998.
%H A099390 J. Propp, <a href="http://jamespropp.org/domino.ps.gz">Dimers and Dominoes</
               a>
%H A099390 <a href="Sindx_Do.html#domino">Index entries for sequences related to 
               dominoes</a>
%F A099390 If m, n even then T(m, n) = Prod[j=1..m/2, Prod[k=1..n/2, 4cos(j*Pi/(m+1))^2 
               + 4cos(k*Pi/(n+1))^2 ]].
%e A099390 0, 1, 0, 1, 0, 1,
%e A099390 1, 2, 3, 5, 8, 13,
%e A099390 0, 3, 0, 11, 0, 41,
%e A099390 1, 5,11, 36, 95, 281,
%e A099390 0, 8, 0, 95, 0,1183,
%e A099390 1,13,41,281,1183,6728,
%Y A099390 See also A004003 for more literature on the dimer problem.
%Y A099390 Rows 2-12 (without zeros) are A000045, A001835, A005178, A003775, A028468, 
               A028469, A028470, A028471, A028472, A028473, A028474.
%Y A099390 Main diagonal is A004003.
%Y A099390 Cf. A103997, A103999.
%Y A099390 Sequence in context: A103438 A167279 A068920 this_sequence A124031 A049600 
               A004542
%Y A099390 Adjacent sequences: A099387 A099388 A099389 this_sequence A099391 A099392 
               A099393
%K A099390 tabl,nonn
%O A099390 1,5
%A A099390 Ralf Stephan, Oct 16 2004
%E A099390 Corrected broken URL's. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jan 06 2009
%E A099390 Fixed old link and added link to results page. - Frans Faase (faase009(AT)planet.nl), 
               Feb 04 2009