A008385 Coordination sequence for A_5 lattice.

1, 30, 240, 1010, 2970, 7002, 14240, 26070, 44130, 70310, 106752, 155850, 220250, 302850, 406800, 535502, 692610, 882030, 1107920, 1374690, 1687002, 2049770, 2468160, 2947590, 3493730, 4112502, 4810080, 5592890, 6467610, 7441170, 8520752

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

Sequence in context: A196412 A081779 A069487 * A061167 A189495 A138404

Adjacent sequences: A008382 A008383 A008384 * A008386 A008387 A008388

Keyword

nonn,easy

Author

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

Status

approved