|
| |
|
|
A035602
|
|
Number of points of L1 norm 8 in cubic lattice Z^n.
|
|
3
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013
J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
|
|
|
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 (Abstract, pdf, ps).
Index to sequences with linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
|
|
|
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
|
|
|
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
|
|
|
MATHEMATICA
|
CoefficientList[Series[2*x*(1+x)^7/(1-x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)
|
|
|
PROG
|
(PARI) a(n)=2*n^2*(n^6+28*n^4+154*n^2+132)/315 \\ Charles R Greathouse IV, Dec 07 2011
(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
|
|
|
CROSSREFS
|
Cf. A035596-A035607.
Sequence in context: A053054 A008512 A179074 * A158040 A202746 A212797
Adjacent sequences: A035599 A035600 A035601 * A035603 A035604 A035605
|
|
|
KEYWORD
|
nonn,easy,changed
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
