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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 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 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 Cf. A110907, A175110. Sequence in context: A247406 A229588 A334121 * A035099 A065255 A300920 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 March 4 10:39 EST 2024. Contains 370528 sequences. (Running on oeis4.)