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A117216 Number of points in the standard root system version of the D_4 lattice having L_infinity norm n. 6
1, 40, 272, 888, 2080, 4040, 6960, 11032, 16448, 23400, 32080, 42680, 55392, 70408, 87920, 108120, 131200, 157352, 186768, 219640, 256160, 296520, 340912, 389528, 442560, 500200, 562640, 630072, 702688, 780680, 864240, 953560, 1048832, 1150248 (list; graph; refs; listen; history; text; internal format)
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
G. Nebe and N. J. A. Sloane, Home page for this lattice
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;
a(n) = 8*n*(1+4*n^2) = 2*A144965(n), n>0 (bisection of A035878 and A105374). (End)
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
Sequence in context: A247406 A229588 A334121 * A035099 A065255 A300920
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

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Last modified March 4 10:39 EST 2024. Contains 370528 sequences. (Running on oeis4.)