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A007900
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Coordination sequence for D_4 lattice.
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1
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1, 24, 144, 456, 1056, 2040, 3504, 5544, 8256, 11736, 16080, 21384, 27744, 35256, 44016, 54120, 65664, 78744, 93456, 109896, 128160, 148344, 170544, 194856, 221376, 250200, 281424, 315144, 351456
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
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LINKS
| Index entries for sequences related to D_4 lattice
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
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FORMULA
| G.f.: (1+54*x^2+20*x+20*x^3+x^4)/(1-x)^4.
G.f. for coordination sequence of D_n lattice: (Sum(binomial(2*n, 2*i)*z^i, i=0..n)-2*n*z*(1+z)^(n-2))/(1-z)^n.
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MAPLE
| if n=0 then 1 else 8*n*(2*n^2+1); fi;
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CROSSREFS
| A row of array A103903.
Sequence in context: A205343 A199827 A076835 * A158874 A059593 A200194
Adjacent sequences: A007897 A007898 A007899 * A007901 A007902 A007903
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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