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A022152 Coordination sequence for root lattice B_10. 4
1, 200, 7760, 122264, 1099040, 6728168, 31208560, 117555640, 376977472, 1064088840, 2708805776, 6332774360, 13786237280, 28250329640, 54959921840, 102213292024, 182747113600, 315568484680, 528350005968, 860509231640, 1367110174112, 2123741938280, 3232547993840 (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 (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

a(0)=1; for n>0, a(n) = ( 2704*n^9 - 6024*n^8 + 51648*n^7 - 80976*n^6 + 248304*n^5 - 239736*n^4 + 296672*n^3 - 126864*n^2 + 43272*n ) / 945. - Ralf Stephan, Apr 28 2004

G.f.: (x^10 +1150*x^9 +19629*x^8 +114600*x^7 +291410*x^6 +350196*x^5 +201810*x^4 +53544*x^3 +5805*x^2 +190*x +1) / (x -1)^10. - Colin Barker, Nov 18 2012

MATHEMATICA

CoefficientList[Series[(x^10 + 1150 x^9 + 19629 x^8 + 114600 x^7 + 291410 x^6 + 350196 x^5 + 201810 x^4 + 53544 x^3 + 5805 x^2 + 190 x + 1)/(x - 1)^10, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 200, 7760, 122264, 1099040, 6728168, 31208560, 117555640, 376977472, 1064088840, 2708805776}, 30] (* Harvey P. Dale, Sep 16 2019 *)

PROG

(MAGMA) [1] cat [(2704*n^9-6024*n^8+51648*n^7-80976*n^6+248304*n^5-239736*n^4+296672*n^3 -126864*n^2+43272*n)/945: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013

CROSSREFS

Sequence in context: A199534 A035747 A219414 * A249238 A230966 A221039

Adjacent sequences:  A022149 A022150 A022151 * A022153 A022154 A022155

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 31 22:35 EDT 2020. Contains 334756 sequences. (Running on oeis4.)