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A117216 Number of points in the standard root system version of the D_4 lattice having L_infinity norm n. 5
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,...] [From 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 sequences related to D_4 lattice

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

FORMULA

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). [From R. J. Mathar, Feb 03 2010, Feb 13 2010]

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

Cf. A110907, A175110.

Sequence in context: A115170 A247406 A229588 * A035099 A065255 A061993

Adjacent sequences:  A117213 A117214 A117215 * A117217 A117218 A117219

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 August 21 23:43 EDT 2017. Contains 290940 sequences.