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

0,2

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).

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]

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 *)

Crossrefs

A row of array A103903.

Sequence in context: A271672 A204390 A343295 * A221127 A262788 A319294

Adjacent sequences: A008373 A008374 A008375 * A008377 A008378 A008379

Keyword

nonn,easy

Author

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

Extensions

More terms from Vincenzo Librandi, Oct 15 2013

Status

approved