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A019560 Coordination sequence for C_4 lattice. 6
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 (list; graph; refs; listen; history; text; internal format)
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.

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 A232051 A247927

Adjacent sequences:  A019557 A019558 A019559 * A019561 A019562 A019563

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 19 15:49 EDT 2018. Contains 316365 sequences. (Running on oeis4.)