OFFSET
0,2
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, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256.
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
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(n) = n*(715*n^6 + 6006*n^4 + 10395*n^2 + 3044)/280, a(0) = 1.
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.: (1 + 64*x + 784*x^2 + 3136*x^3 + 4900*x^4 + 3136*x^5 + 784*x^6 + 64*x^7 + x^8)/(1-x)^8. - Colin Barker, Sep 26 2012
MAPLE
1, seq(n*(715*n^6 + 6006*n^4 +10395*n^2 +3044)/280, n=1..40);
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 */
(Magma) [1] cat [n*(715*n^6 + 6006*n^4 +10395*n^2 +3044)/280: n in [1..40]]; // G. C. Greubel, May 26 2023
(SageMath) [n*(715*n^6 + 6006*n^4 +10395*n^2 +3044)//280 +int(n==0) for n in range(41)] # G. C. Greubel, May 26 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved