The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A035598 Number of points of L1 norm 4 in cubic lattice Z^n. 4
 0, 2, 16, 66, 192, 450, 912, 1666, 2816, 4482, 6800, 9922, 14016, 19266, 25872, 34050, 44032, 56066, 70416, 87362, 107200, 130242, 156816, 187266, 221952, 261250, 305552, 355266, 410816, 472642, 541200, 616962, 700416, 792066 (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 (5,-10,10,-5,1). FORMULA a(n) = 2*n^2*(n^2 + 2)/3. - Frank Ellermann, Mar 16 2002 G.f.: 2*x*(1+x)^3/(1-x)^5. - Colin Barker, Apr 15 2012 a(n) = 2*A014820(n-1). - R. J. Mathar, Dec 10 2013 a(n) = a(n-1) + A035597(n) + A035597(n-1). - Bruce J. Nicholson, Mar 11 2018 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)^3/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 22 2012 *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 16, 66, 192}, 50] (* Harvey P. Dale, Dec 11 2019 *) PROG (PARI) a(n)=2*n^2*(n^2+2)/3 \\ Charles R Greathouse IV, Dec 07 2011 (MAGMA) [( 2*n^4 +4*n^2 )/3: n in [0..40]]; // Vincenzo Librandi, Apr 22 2012 CROSSREFS Cf. A035596, A035597, A035599, A035600, A035601, A035602, A035603, A035604, A035605, A035606, A035607. Sequence in context: A222381 A110048 A094505 * A167566 A034579 A006733 Adjacent sequences:  A035595 A035596 A035597 * A035599 A035600 A035601 KEYWORD nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)