A008376 Coordination sequence for D_9 lattice.

1, 144, 4194, 50832, 361602, 1801872, 6976866, 22413456, 62407170, 155242640, 352624482, 743284368, 1471858818, 2764261008, 4960898658, 8559218832, 14267189250, 23069454480, 36308034146, 55779559056, 83851169922, 123597332112, 178959948642, 254934282384, 357783327234

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

A row of array A103903.

Programs

Maple

1006/315*n^8+488/15*n^6+1084/15*n^4+10712/315*n^2+2;

Mathematica

CoefficientList[Series[-(x + 1) (x^8 + 134 x^7 + 2800 x^6 + 15386 x^5 + 27742 x^4 + 15386 x^3 + 2800 x^2 + 134 x + 1)/(x - 1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,144,4194,50832,361602,1801872,6976866,22413456,62407170,155242640},30] (* Harvey P. Dale, Jun 05 2023 *)

Formula

G.f.: -(x +1)*(x^8 +134*x^7 +2800*x^6 +15386*x^5 +27742*x^4 +15386*x^3 +2800*x^2 +134*x +1) / (x -1)^9. [Colin Barker, Nov 18 2012]

Extensions

More terms from Vincenzo Librandi, Oct 15 2013