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A007900
Coordination sequence for D_4 lattice.
4
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
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).
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
G.f.: (1+54*x^2+20*x+20*x^3+x^4)/(1-x)^4 = 1+24*x*(x+1)^2/(x-1)^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.
MAPLE
if n=0 then 1 else 8*n*(2*n^2+1); fi;
CROSSREFS
A row of array A103903.
Sequence in context: A326856 A358960 A076835 * A158874 A059593 A200194
KEYWORD
nonn,easy
STATUS
approved