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Search: id:A035597
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| A035597 |
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Number of points of L1 norm 3 in cubic lattice Z^n. |
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+0
5
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| 0, 2, 12, 38, 88, 170, 292, 462, 688, 978, 1340, 1782, 2312, 2938, 3668, 4510, 5472, 6562, 7788, 9158, 10680, 12362, 14212, 16238, 18448, 20850, 23452, 26262, 29288, 32538, 36020, 39742, 43712, 47938, 52428, 57190, 62232, 67562
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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
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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).
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FORMULA
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a(n) = (4n^3 + 2n)/3.
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MAPLE
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f := proc(n, m) local i; sum( 2^i*binomial(n, i)*binomial(m-1, i-1), i=1..min(n, m)); end; # n=dimension, m=norm
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MATHEMATICA
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s=0; lst={s}; Do[s+=n^2+1; AppendTo[lst, s], {n, 1, 6!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 07 2008]
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CROSSREFS
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Sequence in context: A011379 A073404 A141208 this_sequence A000913 A026575 A048349
Adjacent sequences: A035594 A035595 A035596 this_sequence A035598 A035599 A035600
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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