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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
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, 28, 150, 272, 209, 76, 13, 1, 1, 36, 256, 636, 696, 376, 106, 15, 1, 1, 45, 410, 1340, 1980, 1496, 615, 141, 17, 1, 1, 55, 625, 2600, 5000, 5032, 2850, 939, 181, 19, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

LINKS

Table of n, a(n) for n=0..66.

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (A_sq of Section 6).

M. Bousquet-Mélou, New enumerative results on two-dimensional directed animals

FORMULA

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

EXAMPLE

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

MATHEMATICA

nmax = 10;

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

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

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

Table[row[n], {n, 0, nmax}] // Flatten (* Jean-François Alcover, Jul 24 2018 *)

CROSSREFS

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

Sequence in context: A129818 A085478 A123970 * A145904 A273350 A278132

Adjacent sequences:  A055895 A055896 A055897 * A055899 A055900 A055901

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, Jun 13 2000

STATUS

approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)