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A035602
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Number of points of L1 norm 8 in cubic lattice Z^n.
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2
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0, 2, 32, 258, 1408, 5890, 20256, 59906, 157184, 374274, 822560, 1690370, 3281280, 6065410, 10746400, 18347010, 30316544, 48663554, 76117536, 116323586, 174074240, 255582978, 368804128, 523804162, 733189632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
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LINKS
| J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
Index to sequences with linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
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FORMULA
| a(n)= ( 2*n^8 +8*7*n^6 +4*7*11*n^4 +8*3*11*n^2 )/(5*7*9). - Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Mar 16 2002
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MAPLE
| f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm
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PROG
| (PARI) a(n)=2*n^2*(n^6+28*n^4+154*n^2+132)/315 \\ Charles R Greathouse IV, Dec 07 2011
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CROSSREFS
| Cf. A035596-A035607.
Sequence in context: A053054 A008512 A179074 * A158040 A202746 A203017
Adjacent sequences: A035599 A035600 A035601 * A035603 A035604 A035605
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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