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A008399 Coordination sequence for E_6 lattice. 2
1, 72, 1062, 6696, 26316, 77688, 189810, 405720, 785304, 1408104, 2376126, 3816648, 5885028, 8767512, 12684042, 17891064, 24684336, 33401736, 44426070, 58187880, 75168252, 95901624, 120978594, 151048728, 186823368, 229078440, 278657262, 336473352, 403513236 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 9*n*(13*n^2+7)*(n^2+1)/5 for n >= 1.

Bacher et al. give a g.f.

G.f.: (x^6+66*x^5+645*x^4+1384*x^3+645*x^2+66*x+1)/(x-1)^6 = 1+18*x *(4+35*x+78*x^2+35*x^3+4*x^4) /(1-x)^6. - Colin Barker, Sep 26 2012

MAPLE

117/5*n^5+36*n^3+63/5*n;

CROSSREFS

Cf. A019557, A019558, A008397, A008340.

Sequence in context: A019562 A250423 A250650 * A232573 A022148 A192847

Adjacent sequences:  A008396 A008397 A008398 * A008400 A008401 A008402

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and J. H. Conway

STATUS

approved

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Last modified July 16 13:35 EDT 2020. Contains 335788 sequences. (Running on oeis4.)