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A055898 Triangle: Number of directed site animals on a square lattice with n+1 total sites and k sites supported in one particular way. 9

%I

%S 1,1,1,1,3,1,1,6,5,1,1,10,16,7,1,1,15,39,31,9,1,1,21,81,101,51,11,1,1,

%T 28,150,272,209,76,13,1,1,36,256,636,696,376,106,15,1,1,45,410,1340,

%U 1980,1496,615,141,17,1,1,55,625,2600,5000,5032,2850,939,181,19,1,1

%N Triangle: Number of directed site animals on a square lattice with n+1 total sites and k sites supported in one particular way.

%D M. Bousquet-Mélou, New enumerative results on two-dimensional directed animals, Discr. Math., 180 (1998), 73-106.

%H A. J. Guttmann, <a href="http://www.ms.unimelb.edu.au/~tonyg/articles/viennafinal.pdf">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189 (A_sq of Section 6).

%H M. Bousquet-Mélou, <a href="http://www.labri.fr/Perso/~bousquet/Articles/Diriges/ani.ps.gz">New enumerative results on two-dimensional directed animals</a>

%F G.f.: A(x, y)=(1/2x)((1-(4x/((1+x)(1+x-xy))))^(-1/2) - 1).

%e 1; 1,1; 1,3,1; 1,6,5,1; 1,10,16,7,1; ...

%t nmax = 10;

%t A[x_, y_] = (1/2) x ((1 - (4 x/((1 + x) (1 + x - x y))))^(-1/2) - 1);

%t g = A[x, y] + O[x]^(nmax+3);

%t row[n_] := CoefficientList[Coefficient[g, x, n+2], y];

%t Table[row[n], {n, 0, nmax}] // Flatten (* _Jean-François Alcover_, Jul 24 2018 *)

%Y Row sums give A005773. Columns 0-8: A000012, A000217, A011863(n-1), A055899-A055904. Cf. A055905, A055907.

%K nonn,tabl

%O 0,5

%A _Christian G. Bower_, Jun 13 2000

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Last modified August 19 04:34 EDT 2019. Contains 326109 sequences. (Running on oeis4.)