Search: id:A035597
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%I A035597
%S A035597 0,2,12,38,88,170,292,462,688,978,1340,1782,2312,2938,3668,4510,
%T A035597 5472,6562,7788,9158,10680,12362,14212,16238,18448,20850,23452,
%U A035597 26262,29288,32538,36020,39742,43712,47938,52428,57190,62232,67562
%N A035597 Number of points of L1 norm 3 in cubic lattice Z^n.
%D A035597 J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information 
               Processing Letters, 76, no. 1-2 (2000), 39-44.
%H A035597 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination 
               Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http:/
               /www.research.att.com/~njas/doc/ldl7.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.ps">ps</a>).
%H A035597 J. H. Conway and N. J. A. Sloane, <a href="http://dx.doi.org/10.1098/
               rspa.1997.0126">Low-dimensional lattices. VII. Coordination sequences</
               a>, Proc. Roy. Soc. Lond. A 458 (1996) 2369-2389. [From R. J. Mathar 
               (matahr(AT)strw.leidenuniv.nl), Dec 05 2009]
%H A035597 Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">
               Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 
               (1-2) (2000) 39-44. [From R. J. Mathar (matahr(AT)strw.leidenuniv.nl), 
               Dec 05 2009]
%F A035597 a(n) = (4n^3 + 2n)/3.
%F A035597 a(n) = 2*A005900(n). [From R. J. Mathar (matahr(AT)strw.leidenuniv.nl), 
               Dec 05 2009]
%p A035597 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
%t A035597 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]
%Y A035597 Sequence in context: A011379 A073404 A141208 this_sequence A000913 A026575 
               A048349
%Y A035597 Adjacent sequences: A035594 A035595 A035596 this_sequence A035598 A035599 
               A035600
%K A035597 nonn,easy,nice,new
%O A035597 0,2
%A A035597 N. J. A. Sloane (njas(AT)research.att.com).

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