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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Row 7 of A103881.

Programs

Magma

[1] cat [2 +n^2*(143*n^4 +770*n^2 +707)/30: n in [1..40]]; // 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 *)

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

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