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A035597 Number of points of L1 norm 3 in cubic lattice Z^n. 9
0, 2, 12, 38, 88, 170, 292, 462, 688, 978, 1340, 1782, 2312, 2938, 3668, 4510, 5472, 6562, 7788, 9158, 10680, 12362, 14212, 16238, 18448, 20850, 23452, 26262, 29288, 32538, 36020, 39742, 43712, 47938, 52428, 57190, 62232, 67562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is the partial sums of A069894. - J. M. Bergot, May 31 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

J. H. Conway and N. J. A. Sloane, Low-dimensional lattices. VII. Coordination sequences, Proc. Roy. Soc. Lond. A 458 (1996) 2369-2389.

M. Janjic, On a class of polynomials with integer coefficients, JIS 11 (2008) 08.5.2

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 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. [From R. J. Mathar, Dec 05 2009]

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = (4*n^3 + 2*n)/3.

a(n) = 2*A005900(n). - R. J. Mathar, Dec 05 2009

a(0)=0, a(1)=2, a(2)=12, a(3)=38, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: (2*x*(x+1)^2)/(x-1)^4. - Harvey P. Dale, Sep 18 2011

a(n) = -a(-n), a(n+1) = A097869(4n+3) = A084570(2n+1). - Bruno Berselli, Sep 20 2011

MAPLE

f := proc(n, m) local i; sum( 2^i*binomial(n, i)*binomial(m-1, i-1), i=1..min(n, m)); end; # n=dimension, m=norm

MATHEMATICA

s=0; lst={s}; Do[s+=n^2+1; AppendTo[lst, s], {n, 1, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)

Table[(4n^3+2n)/3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 2, 12, 38}, 41] (* Harvey P. Dale, Sep 18 2011 *)

PROG

(MAGMA) [(4*n^3 + 2*n)/3: n in [0..40]]; // Vincenzo Librandi, Sep 19 2011

CROSSREFS

Sequence in context: A192385 A294464 A185788 * A000913 A026575 A048349

Adjacent sequences:  A035594 A035595 A035596 * A035598 A035599 A035600

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 20 16:14 EST 2018. Contains 299380 sequences. (Running on oeis4.)