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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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8
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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; 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
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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).
J. H. Conway and N. J. A. Sloane, Low-dimensional lattices. VII. Coordination sequences, Proc. Roy. Soc. Lond. A 458 (1996) 2369-2389. [From R. J. Mathar, Dec 05 2009]
Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44. [From R. J. Mathar, Dec 05 2009]
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n) = (4*n^3 + 2*n)/3.
a(n) = 2*A005900(n). - R. J. Mathar, Dec 05 2009
a(0)=0, a(1)=2, a(2)=12, a(3)=38, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: (2*x*(x+1)^2)/(x-1)^4. - Harvey P. Dale, Sep 18 2011
a(n) = -a(-n), a(n+1) = A097869(4n+3) = A084570(2n+1). - Bruno Berselli, Sep 20 2011
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MAPLE
| 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
| s=0; lst={s}; Do[s+=n^2+1; AppendTo[lst, s], {n, 1, 6!, 2}]; lst [From Vladimir Orlovsky, Nov 07 2008]
Table[(4n^3+2n)/3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 2, 12, 38}, 41] (* From Harvey P. Dale, Sep 18 2011 *)
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PROG
| (MAGMA) [(4*n^3 + 2*n)/3: n in [0..40]]; // Vincenzo Librandi, Sep 19 2011
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CROSSREFS
| Sequence in context: A169630 A192385 A185788 * A000913 A026575 A048349
Adjacent sequences: A035594 A035595 A035596 * A035598 A035599 A035600
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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