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A059712
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Number of stacked directed animals on the square lattice.
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0
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1, 2, 6, 19, 63, 213, 729, 2513, 8703, 30232, 105236, 366849, 1280131, 4470354, 15619386, 54595869, 190891131, 667590414, 2335121082, 8168950665, 28580354769, 100000811433, 349918126509, 1224476796543, 4285005630969
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The generating function is simply derived from the generating function for directed animals. A triangular lattice version exists.
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REFERENCES
| M. Bousquet-Melou and A. Rechnitzer, Lattice animals and heaps of dimers, Discrete Math. 258 (2002), no. 1-3, 235-274.
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LINKS
| M. Bousquet-Melou and A. Rechnitzer, Lattice animals and heaps of dimers
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FORMULA
| G.f.: ((1-2x)(1-3x)-(1-4x)sqrt((1-3x)(1+x)))/(2x(2-7x))
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MAPLE
| gf := ((1-2*x)*(1-3*x)-(1-4*x)*sqrt((1-3*x)*(1+x)))/(2*x*(2-7*x)): s := series(gf, x, 50): for i from 1 to 100 do printf(`%d, `, coeff(s, x, i)) od:
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CROSSREFS
| Directed animals: A005773.
Sequence in context: A026012 A191993 A120900 * A059713 A109262 A006724
Adjacent sequences: A059709 A059710 A059711 * A059713 A059714 A059715
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KEYWORD
| nonn
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AUTHOR
| Mireille Bousquet-Melou (bousquet(AT)labri.u-bordeaux.fr), Feb 08 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 09 2001
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