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A007900 Coordination sequence for D_4 lattice. 3
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; 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

Table of n, a(n) for n=0..28.

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 sequences related to D_4 lattice

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: A316928 A326856 A076835 * A158874 A059593 A200194

Adjacent sequences:  A007897 A007898 A007899 * A007901 A007902 A007903

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)