OFFSET
0,2
COMMENTS
This lattice consists of all points (w,x,y,z) where w,x,y,z are integers with an even sum.
The L_infinity norm of a vector is the largest component in absolute value.
Equals binomial transform of [1, 39, 193, 191, 1, -1, 1, -1, 1, ...]. - Gary W. Adamson, Feb 05 2010
REFERENCES
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, Chap. 4.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
G. Nebe and N. J. A. Sloane, Home page for this lattice
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
From R. J. Mathar, Feb 03 2010, Feb 13 2010: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n>4;
G.f.: (1 + 36*x + 118*x^2 + 36*x^3 + x^4)/(1-x)^4. - Colin Barker, May 24 2012
MATHEMATICA
CoefficientList[Series[(1+36*x+118*x^2+36*x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 27 2012 *)
PROG
(Magma) I:=[1, 40, 272, 888, 2080]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 27 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 15 2008
EXTENSIONS
a(2) corrected and sequence extended by R. J. Mathar, Feb 03 2010, Feb 13 2010
STATUS
approved