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A035599 Number of points of L1 norm 5 in cubic lattice Z^n. 3
0, 2, 20, 102, 360, 1002, 2364, 4942, 9424, 16722, 28004, 44726, 68664, 101946, 147084, 207006, 285088, 385186, 511668, 669446, 864008, 1101450, 1388508, 1732590, 2141808, 2625010, 3191812, 3852630, 4618712, 5502170, 6516012 (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

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 (6,-15,20,-15,6,-1).

FORMULA

a(n) = (4*n^4+20*n^2+6)*n/15. - Frank Ellermann, Mar 16 2002

G.f.: 2*x*(1+x)^4/(1-x)^6. - Colin Barker, Mar 19 2012

a(n) = 2*A069038(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)^4/(1-x)^6, {x, 0, 33}], x] (* Vincenzo Librandi, Apr 23 2012 *)

PROG

(PARI) a(n)=(4*n^5+20*n^3+6*n)/15 \\ Charles R Greathouse IV, Dec 07 2011

(MAGMA) [(4*n^4+20*n^2+6)*n/15: n in [0..30]]; // Vincenzo Librandi, Apr 23 2012

CROSSREFS

Cf. A035596-A035607.

Sequence in context: A086755 A107483 A220856 * A222556 A103101 A267678

Adjacent sequences:  A035596 A035597 A035598 * A035600 A035601 A035602

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)