|
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
REFERENCES
| M. Bousquet-M\'{e}lou, New enumerative results on two-dimensional directed animals, Discr. Math., 180 (1998), 73-106.
|
|
|
LINKS
| A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (A_sq of Section 6).
M. Bousquet-M\'{e}lou, 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; ...
|
|
|
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 A203950 A159572
Adjacent sequences: A055895 A055896 A055897 * A055899 A055900 A055901
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Jun 13 2000
|
| |
|
|
