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Search: id:A055898
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| A055898 |
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Triangle: Number of directed site animals on a square lattice with n+1 total sites and k sites supported in one particular way. |
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+0
10
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| 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; listen)
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OFFSET
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0,5
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REFERENCES
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M. Bousquet-M\'{e}lou, New enumerative results on two-dimensional directed animals, Discr. Math., 180 (1998), 73-106.
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LINKS
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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
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FORMULA
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G.f.: A(x, y)=(1/2x)((1-(4x/((1+x)(1+x-xy))))^(-1/2) - 1).
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EXAMPLE
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1; 1,1; 1,3,1; 1,6,5,1; 1,10,16,7,1; ...
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CROSSREFS
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Row sums give A005773. Columns 0-8: A000012, A000217, A011863(n-1), A055899-A055904. Cf. A055905, A055907.
Sequence in context: A085478 A123970 A129818 this_sequence A145904 A159572 A035582
Adjacent sequences: A055895 A055896 A055897 this_sequence A055899 A055900 A055901
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jun 13 2000
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