A035603 Number of points of L1 norm 9 in cubic lattice Z^n.

0, 2, 36, 326, 1992, 9290, 35436, 115598, 332688, 864146, 2060980, 4573910, 9545560, 18892250, 35704060, 64797470, 113461024, 192441122, 317222212, 509663334, 800061160, 1229718378, 1854105484, 2746713774, 4003707568

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. - 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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = (4*n^9 + 168*n^7 + 1596*n^5 + 3272*n^3 + 630*n)/(5*7*9*9). - Frank Ellermann, Mar 16 2002

G.f.: 2*x*(1+x)^8/(1-x)^10. - Colin Barker, Apr 15 2012

a(n) = 2*A099196(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)^8/(1-x)^10, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 24 2012 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 2, 36, 326, 1992, 9290, 35436, 115598, 332688, 864146}, 30] (* Harvey P. Dale, Jan 17 2021 *)

Prog

(PARI) a(n)=(4*n^9+168*n^7+1596*n^5+3272*n^3+630*n)/2835 \\ Charles R Greathouse IV, Dec 07 2011
(Magma) [(4*n^9+168*n^7+1596*n^5+3272*n^3+630*n)/2835: n in [0..30]]; // Vincenzo Librandi, Apr 24 2012

Crossrefs

Cf. A035596-A035607.

Sequence in context: A082636 A242533 A273325 * A126735 A229679 A119582

Adjacent sequences: A035600 A035601 A035602 * A035604 A035605 A035606

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved