A008389 Coordination sequence for A_7 lattice.

1, 56, 812, 5768, 26474, 91112, 256508, 623576, 1356194, 2703512, 5025692, 8823080, 14768810, 23744840, 36881420, 55599992, 81659522, 117206264, 164826956, 227605448, 309182762, 413820584, 546468188, 712832792, 919453346

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 (7,-21,35,-35,21,-7,1).

Formula

G.f.: (1+x)*(1+48*x+393*x^2+832*x^3+393*x^4+48*x^5+x^6)/(1-x)^7. - Colin Barker, Sep 26 2012

a(n) = 2 + n^2*(143*n^4 +770*n^2 +707)/30 with n>0, a(0)=1. - Bruno Berselli, Sep 26 2012

E.g.f.: -1 + (1/30)*(60 +1620*x +10530*x^2 +17490*x^3 +10065*x^4 +2145*x^5 +143*x^6)*exp(x). - G. C. Greubel, May 26 2023

Maple

1, seq(2 +n^2*(143*n^4 +770*n^2 +707)/30, n=1..50);

Mathematica

Table[n^2*(143*n^4 +770*n^2 +707)/30 +2 -Boole[n==0], {n, 0, 40}] (* G. C. Greubel, May 26 2023 *)

Prog

(Magma) [1] cat [2 +n^2*(143*n^4 +770*n^2 +707)/30: n in [1..40]]; // G. C. Greubel, May 26 2023
(SageMath) [2 +n^2*(143*n^4 +770*n^2 +707)/30 -int(n==0) for n in range(41)] # G. C. Greubel, May 26 2023

Crossrefs

Row 7 of A103881.

Sequence in context: A285155 A278197 A182866 * A338002 A351410 A219937

Adjacent sequences: A008386 A008387 A008388 * A008390 A008391 A008392

Keyword

nonn,easy

Author

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

Status

approved