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A035598 Number of points of L1 norm 4 in cubic lattice Z^n. 4

%I

%S 0,2,16,66,192,450,912,1666,2816,4482,6800,9922,14016,19266,25872,

%T 34050,44032,56066,70416,87362,107200,130242,156816,187266,221952,

%U 261250,305552,355266,410816,472642,541200,616962,700416,792066

%N Number of points of L1 norm 4 in cubic lattice Z^n.

%H Vincenzo Librandi, <a href="/A035598/b035598.txt">Table of n, a(n) for n = 0..1000</a>

%H 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://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - _N. J. A. Sloane_, Feb 13 2013

%H M. Janjic, B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5.

%H 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.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = 2*n^2*(n^2 + 2)/3. - _Frank Ellermann_, Mar 16 2002

%F G.f.: 2*x*(1+x)^3/(1-x)^5. - _Colin Barker_, Apr 15 2012

%F a(n) = 2*A014820(n-1). - _R. J. Mathar_, Dec 10 2013

%F a(n) = a(n-1) + A035597(n) + A035597(n-1). - _Bruce J. Nicholson_, Mar 11 2018

%p 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

%t CoefficientList[Series[2*x*(1+x)^3/(1-x)^5,{x,0,40}],x] (* _Vincenzo Librandi_, Apr 22 2012 *)

%o (PARI) a(n)=2*n^2*(n^2+2)/3 \\ _Charles R Greathouse IV_, Dec 07 2011

%o (MAGMA) [( 2*n^4 +4*n^2 )/3: n in [0..40]]; // _Vincenzo Librandi_, Apr 22 2012

%Y Cf. A035596, A035597, A035599, A035600, A035601, A035602, A035603, A035604, A035605, A035606, A035607.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)