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).
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (21*n^4 + 35*n^2 + 4)/2, a(0) = 1.
G.f.: (1+x)*(1+24*x+76*x^2+24*x^3+x^4)/(1-x)^5. - Colin Barker, Apr 13 2012
E.g.f.: (1/2)*(-2 + (4 + 56*x + 182*x^2 + 126*x^3 + 21*x^4)*exp(x)). - G. C. Greubel, May 26 2023
MAPLE
1, seq((21*n^4 +35*n^2 +4)/2, n=1..50);
MATHEMATICA
Table[n^2*(21*n^2 +35)/2 +2 -Boole[n==0], {n, 0, 50}] (* G. C. Greubel, May 26 2023 *)
PROG
(Maxima) A008385[n]:=21/2*n^4+35/2*n^2+2$
makelist(A008385[n], n, 0, 30); /* Martin Ettl, Oct 26 2012 */
(Magma) [n eq 0 select 1 else (21*n^4 +35*n^2 +4)/2: n in [0..50]]; // G. C. Greubel, May 26 2023
(SageMath) [n^2*(21*n^2 +35)/2 +2 -int(n==0) for n in range(51)] # G. C. Greubel, May 26 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved