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A008391
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Coordination sequence for A_8 lattice.
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2
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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
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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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). [From 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]
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MAPLE
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143/56*n^7+429/20*n^5+297/8*n^3+761/70*n;
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MATHEMATICA
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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]](* From Harvey P. Dale, Mar 04 2012 *)
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PROG
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(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 */
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CROSSREFS
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Sequence in context: A168194 A200556 A128800 * A037251 A008659 A187303
Adjacent sequences: A008388 A008389 A008390 * A008392 A008393 A008394
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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More terms from Harvey P. Dale, Mar 04 2012
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STATUS
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approved
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