A035600 Number of points of L1 norm 6 in cubic lattice Z^n.
0, 2, 24, 146, 608, 1970, 5336, 12642, 27008, 53154, 97880, 170610, 284000, 454610, 703640, 1057730, 1549824, 2220098, 3116952, 4298066, 5831520, 7796978, 10286936, 13408034, 17282432, 22049250, 27866072, 34910514, 43381856, 53502738, 65520920, 79711106
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. - From _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 (7,-21,35,-35,21,-7,1).
Programs
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Magma
[( 4*n^6 +40*n^4 +46*n^2 )/45: n in [0..30]]; // Vincenzo Librandi, Apr 23 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)^5/(1-x)^7,{x,0,33}],x] (* Vincenzo Librandi, Apr 23 2012 *) -
PARI
a(n)=(4*n^6+40*n^4+46*n^2)/45 \\ Charles R Greathouse IV, Dec 07 2011
Formula
a(n) = (4*n^6 + 40*n^4 + 46*n^2)/45. - Frank Ellermann, Mar 16 2002
G.f.: 2*x*(1+x)^5/(1-x)^7. - Colin Barker, Apr 15 2012
a(n) = 2*A069039(n). - R. J. Mathar, Dec 10 2013