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A022153 Coordination sequence for root lattice B_11. 4
1, 242, 11242, 210474, 2224178, 15804866, 83999962, 358159802, 1285951458, 4025098770, 11267030346, 28752157898, 67886298898, 150029971938, 313233102138, 622431249242, 1184409984450, 2169185665330, 3839847763114, 6593364255082, 11015371578354, 17952558422018 (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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(0)=1; for n>0, a(n) = ( 16296*n^10 - 40520*n^9 + 422820*n^8 - 772320*n^7 + 3019968*n^6 - 3688440*n^5 + 6425580*n^4 - 4306480*n^3 + 2872836*n^2 - 547740*n + 28350 ) / 14175. - Ralf Stephan, Apr 28 2004

G.f.: -(x^11 +1551*x^10 +32659*x^9 +242517*x^8 +812570*x^7 +1346534*x^6 +1139446*x^5 +487674*x^4 +99957*x^3 +8635*x^2 +231*x +1) / (x -1)^11. - Colin Barker, Nov 18 2012

MATHEMATICA

CoefficientList[Series[-(x^11 + 1551 x^10 + 32659 x^9 + 242517 x^8 + 812570 x^7 + 1346534 x^6+1139446 x^5 + 487674 x^4 + 99957 x^3 + 8635 x^2 + 231 x + 1)/(x - 1)^11, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *)

PROG

(MAGMA) [1] cat [(16296*n^10 -40520*n^9 +422820*n^8 -772320*n^7 +3019968*n^6 -3688440*n^5 +6425580*n^4 -4306480*n^3 +2872836*n^2 -547740*n +28350)/14175: n in [1..30]]; // Vincenzo Librandi_, Oct 17 2013

CROSSREFS

Sequence in context: A006601 A283723 A035748 * A194788 A055554 A214105

Adjacent sequences:  A022150 A022151 A022152 * A022154 A022155 A022156

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 30 05:08 EDT 2020. Contains 334712 sequences. (Running on oeis4.)