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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 * A202593 A293104 A267750 Adjacent sequences:  A008394 A008395 A008396 * A008398 A008399 A008400 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 22 11:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)