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A022150 Coordination sequence for root lattice B_8. 4
1, 128, 3264, 34624, 216448, 954880, 3301952, 9556160, 24165120, 54993792, 115021760, 224533056, 413862016, 726758656, 1224437056, 1990370240, 3135895040, 4806690432, 7190192832, 10524011840, 15105409920, 21301909504, 29563091008, 40433645248, 54567743744 (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

Vincenzo Librandi, 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.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(0) = 1; for n>0, a(n) = (3968*n^7 - 6720*n^6 + 35840*n^5 - 36960*n^4 + 60032*n^3 - 26880*n^2 + 11040*n)/315 . - Philippe Deléham, Feb 20 2004

G.f.: (x^8 +568*x^7 +5852*x^6 +18888*x^5 +23750*x^4 +12040*x^3 +2268*x^2 +120*x +1)/(x -1)^8. - Colin Barker, Nov 18 2012

MATHEMATICA

CoefficientList[Series[(x^8 + 568 x^7 + 5852 x^6 + 18888 x^5 + 23750 x^4 + 12040 x^3 + 2268 x^2 + 120 x + 1)/(x - 1)^8, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)

PROG

(MAGMA) [1] cat [(3968*n^7-6720*n^6+35840*n^5-36960*n^4+60032*n^3 -26880*n^2+11040*n)/315: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013

CROSSREFS

Sequence in context: A297613 A250565 A264383 * A269001 A191899 A191495

Adjacent sequences:  A022147 A022148 A022149 * A022151 A022152 A022153

KEYWORD

nonn,easy

AUTHOR

mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)

STATUS

approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)