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A008340 Coordination sequence for E_8 lattice. 4
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; text; internal format)
OFFSET
0,2
REFERENCES
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
LINKS
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
G. Nebe and N. J. A. Sloane, Home page for this lattice
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
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.
G.f.: (x^8 +232*x^7 +24508*x^6 +107224*x^5 +133510*x^4 +55384*x^3 +7228*x^2 +232*x +1)/(x -1)^8 = 1 + 240*x* (1+30*x+231*x^2+556*x^3+447*x^4+102*x^5+x^6) /(1-x)^8. [Colin Barker, Sep 26 2012]
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;
MATHEMATICA
Join[{1}, Table[456/7*n^7-120*n^6+312*n^5-120*n^4-48*n^3+ 240*n^2- 624/7*n, {n, 20}]] (* Harvey P. Dale, Jul 14 2014 *)
CROSSREFS
Sequence in context: A268637 A264317 A270174 * A252183 A251434 A187167
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
The values given by O'Keeffe are incorrect.
STATUS
approved

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Last modified April 19 17:51 EDT 2024. Contains 371797 sequences. (Running on oeis4.)