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

0,2

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).

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

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: A224903 A008512 A179074 * A158040 A202746 A212797

Adjacent sequences: A035599 A035600 A035601 * A035603 A035604 A035605

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved