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A008397 Coordination sequence for E_7 lattice. 3
1, 126, 2898, 25886, 133506, 490014, 1433810, 3573054, 7902594, 15942206, 29896146, 52834014, 88892930, 143501022, 223622226, 338022398, 497556738, 715478526, 1007769170, 1393489566 (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.

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).

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = 148/5*n^6-12/5*n^5+52*n^4+12*n^3+212/5*n^2-48/5*n+2 for n >= 1.

Bacher et al. give a g.f.

G.f.: -(x^7+119*x^6+2037*x^5+8787*x^4+8211*x^3+2037*x^2+119*x+1)/(x-1)^7. [Colin Barker, Sep 26 2012]

MAPLE

a:= n-> `if`(n=0, 1, 148/5*n^6-12/5*n^5+52*n^4+12*n^3+212/5*n^2-48/5*n+2):

seq(a(n), n=0..25);

MATHEMATICA

Join[{1}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {126, 2898, 25886, 133506, 490014, 1433810, 3573054}, 20]] (* Harvey P. Dale, Nov 12 2014 *)

CROSSREFS

Sequence in context: A202398 A113857 A267282 * A329754 A202593 A293104

Adjacent sequences:  A008394 A008395 A008396 * A008398 A008399 A008400

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified August 19 11:12 EDT 2022. Contains 356228 sequences. (Running on oeis4.)