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

0,2

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).

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

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 *)

Crossrefs

Cf. A008414.

Sequence in context: A330829 A240983 A210627 * A250423 A250650 A008399

Adjacent sequences: A019559 A019560 A019561 * A019563 A019564 A019565

Keyword

nonn,easy

Author

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

Status

approved