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
KEYWORD
nonn,easy
AUTHOR
mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake)
STATUS
approved