A019562 Coordination sequence for C_6 lattice.

1, 72, 912, 5336, 20256, 58728, 142000, 301560, 581184, 1038984, 1749456, 2805528, 4320608, 6430632, 9296112, 13104184, 18070656, 24442056, 32497680, 42551640, 54954912, 70097384, 88409904, 110366328, 136485568, 167333640, 203525712, 245728152, 294660576

Offset: 0

Author

Michael Baake (mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de)

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, 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.
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A008414.

Programs

Mathematica

Join[{1}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {72, 912, 5336, 20256, 58728, 142000}, 28]] (* Jean-François Alcover, Dec 08 2018 *)
CoefficientList[Series[(1+66 x+495 x^2+924 x^3+495 x^4+66 x^5+ x^6)/ (-1+x)^6,{x,0,60}],x] (* Harvey P. Dale, Jun 06 2021 *)

Formula

G.f.: (1+6*x+x^2)*(1+60*x+134*x^2+60*x^3+x^4)/(1-x)^6.

a(n) = A008414(2*n). - Seiichi Manyama, Jun 08 2018