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A008391 Coordination sequence for A_8 lattice. 2
1, 72, 1332, 11832, 66222, 271224, 889716, 2476296, 6077196, 13507416, 27717948, 53265960, 96900810, 168278760, 280819260, 452715672, 708113304, 1078467624, 1604095524, 2335932504, 3337508646, 4687156248, 6480461988, 8832976488, 11883194148, 15795816120 (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 (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

a(0)=1, a(1)=72, a(2)=1332, a(3)=11832, a(4)=66222, a(5)=271224, a(6)=889716, a(7)=2476296, a(8)=6077196, a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Mar 04 2012

G.f.: (x^8 + 64*x^7 + 784*x^6 + 3136*x^5 + 4900*x^4 + 3136*x^3 + 784*x^2 + 64*x + 1)/(x - 1)^8. - Colin Barker, Sep 26 2012

MAPLE

143/56*n^7+429/20*n^5+297/8*n^3+761/70*n;

MATHEMATICA

Join[{1}, Table[143/56n^7+429/20n^5+297/8n^3+761/70n, {n, 30}]] (* or *) Join[{1}, LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {72, 1332, 11832, 66222, 271224, 889716, 2476296, 6077196}, 30]](* Harvey P. Dale, Mar 04 2012 *)

PROG

(Maxima)

a[0]:1$

a[1]:72$

a[2]:1332$

a[3]:11832$

a[4]:66222$

a[5]:271224$

a[6]:889716$

a[7]:2476296$

a[8]:6077196$

a[n]:=8*a[n-1]-28*a[n-2]+ 56*a[n-3]- 70*a[n-4]+56*a[n-5]-28*a[n-6]+8*a[n-7]-a[n-8];

makelist(a[n], n, 0, 30); /* Martin Ettl, Oct 26 2012 */

CROSSREFS

Sequence in context: A200556 A239423 A128800 * A292881 A282018 A037251

Adjacent sequences:  A008388 A008389 A008390 * A008392 A008393 A008394

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)