A035602 Number of points of L1 norm 8 in cubic lattice Z^n.
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
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - _N. J. A. Sloane_, Feb 13 2013
- M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
- Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Magma
[(2*n^8+8*7*n^6+4*7*11*n^4+8*3*11*n^2)/315: n in [0..30]]; // Vincenzo Librandi, Apr 24 2012
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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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Mathematica
CoefficientList[Series[2*x*(1+x)^7/(1-x)^9,{x,0,30}],x] (* Vincenzo Librandi, Apr 24 2012 *) -
PARI
a(n)=2*n^2*(n^6+28*n^4+154*n^2+132)/315 \\ Charles R Greathouse IV, Dec 07 2011
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, Mar 16 2002
G.f.: 2*x*(1+x)^7/(1-x)^9. - Colin Barker, Apr 15 2012
a(n) = 2*A099195(n). - R. J. Mathar, Dec 10 2013