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A008340
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Coordination sequence for E_8 lattice.
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3
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1, 240, 9120, 121680, 864960, 4113840, 14905440, 44480400, 114879360, 265422960, 561403680, 1105317840, 2050966080, 3620750640, 6126497760, 9994133520, 15792541440, 24266930160, 36377039520, 53340513360, 76681767360
(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
| T. D. Noe, Table of n, a(n) for n=0..1000
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).
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
| a(n) = if n = 0 then 1 else 456/7*n^7-120*n^6+312*n^5-120*n^4-48*n^3+240*n^2-624/7*n.
Bacher et al. give a g.f.
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MAPLE
| if n = 0 then 1 else 456/7*n^7-120*n^6+312*n^5-120*n^4-48*n^3+240*n^2-624/7*n;
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CROSSREFS
| Cf. A019557, A019558, A008397, A008399.
Sequence in context: A005950 A004536 A145094 * A187167 A023906 A035841
Adjacent sequences: A008337 A008338 A008339 * A008341 A008342 A008343
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KEYWORD
| nonn,easy,nice
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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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EXTENSIONS
| The values given by O'Keeffe are incorrect.
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