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Search: id:A117216
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| A117216 |
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Number of points in the standard root system version of the D_4 lattice having L_infinity norm n. |
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+0
5
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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 (qntmpkt(AT)yahoo.com), Feb 05 2010]
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REFERENCES
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J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, Chap. 4.
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LINKS
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G. Nebe and N. J. A. Sloane, Home page for this lattice
Index entries for sequences related to D_4 lattice
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FORMULA
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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 (mathar(AT)strw.leidenuniv.nl), Feb 03 2010, Feb 13 2010]
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CROSSREFS
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Cf. A110907, A175110.
Adjacent sequences: A117213 A117214 A117215 this_sequence A117217 A117218 A117219
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 15 2008
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EXTENSIONS
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a(2) corrected and sequence extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2010, Feb 13 2010
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