A019560 Coordination sequence for C_4 lattice.

1, 32, 192, 608, 1408, 2720, 4672, 7392, 11008, 15648, 21440, 28512, 36992, 47008, 58688, 72160, 87552, 104992, 124608, 146528, 170880, 197792, 227392, 259808, 295168, 333600, 375232, 420192, 468608

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)

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.

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

a(n) = (32/3)*n*(1 + 2*n^2) for n>0.

G.f.: (1 + 28*x + 70*x^2 + 28*x^3 + x^4)/(1 - x)^4.

G.f. for sequence with interpolated zeros: cosh(8*arctanh(x)) = 1/2*(((1 + x)/(1 - x))^4 + ((1 - x)/(1 + x))^4) = 1 + 32*x^2 + 192*x^4 + 608*x^6 + .... Cf. A057813. - Peter Bala, Apr 09 2017

a(n) = A008412(2*n). - Seiichi Manyama, Jun 08 2018

Mathematica

Join[{1}, Table[(32/3) n (1 + 2 n^2), {n, 30}]] (* Vincenzo Librandi, Apr 10 2017 *)

Prog

(Magma) [1] cat [(32/3)*n*(1 + 2*n^2): n in [1..40]]; // Vincenzo Librandi, Apr 10 2017

Crossrefs

Cf. A103884 (row 4). For coordination sequences of other C_n lattices see A022144 (C_2), A010006 (C3), A019560 - A019564 (C_4 through C_8), A035746 - A035787 (C_9 through C_50).

Cf. A008412, A137513.

Sequence in context: A200840 A208925 A212863 * A130811 A350740 A232051

Adjacent sequences: A019557 A019558 A019559 * A019561 A019562 A019563

Keyword

nonn,easy

Author

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

Status

approved