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A035606 Number of points of L1 norm 12 in cubic lattice Z^n. 4
0, 2, 48, 578, 4672, 28610, 142000, 596610, 2187520, 7159170, 21278640, 58227906, 148321344, 354870594, 803467056, 1732242690, 3575055360, 7094825730, 13591279920, 25216532290, 45443741760, 79749022402 (list; graph; refs; listen; history; text; internal format)
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

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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

FORMULA

From Colin Barker, Apr 15 2012: (Start)

a(n) = 2*n^2*(146430 + 239327*n^2 + 74800*n^4 + 6996*n^6 + 220*n^8 + 2*n^10)/467775.

G.f.: 2*x*(1+x)^11/(1-x)^13. (End)

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)^11/(1-x)^13, {x, 0, 30}], x](* Vincenzo Librandi, Apr 24 2012 *)

PROG

(MAGMA) I:=[0, 2, 48, 578, 4672, 28610, 142000, 596610, 2187520, 7159170, 21278640, 58227906, 148321344]; [n le 13 select I[n] else 13*Self(n-1)-78*Self(n-2)+286*Self(n-3)-715*Self(n-4)+1287*Self(n-5)-1716*Self(n-6)+1716*Self(n-7)-1287*Self(n-8)+715*Self(n-9)-286*Self(n-10)+78*Self(n-11)-13*Self(n-12)+Self(n-13): n in [1..30]]; // Vincenzo Librandi, Apr 24 2012

CROSSREFS

Sequence in context: A051252 A231654 A005429 * A157057 A290690 A013523

Adjacent sequences:  A035603 A035604 A035605 * A035607 A035608 A035609

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)