# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a035599 Showing 1-1 of 1 %I A035599 #52 Dec 30 2023 13:28:24 %S A035599 0,2,20,102,360,1002,2364,4942,9424,16722,28004,44726,68664,101946, %T A035599 147084,207006,285088,385186,511668,669446,864008,1101450,1388508, %U A035599 1732590,2141808,2625010,3191812,3852630,4618712,5502170,6516012 %N A035599 Number of points of L1 norm 5 in cubic lattice Z^n. %H A035599 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 %H A035599 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf). %H A035599 M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - _N. J. A. Sloane_, Feb 13 2013 %H A035599 M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5. %H A035599 Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44. %H A035599 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). %F A035599 a(n) = (4*n^4+20*n^2+6)*n/15. - _Frank Ellermann_, Mar 16 2002 %F A035599 G.f.: 2*x*(1+x)^4/(1-x)^6. - _Colin Barker_, Mar 19 2012 %F A035599 a(n) = 2*A069038(n). - _R. J. Mathar_, Dec 10 2013 %F A035599 From _Shel Kaphan_, Mar 01 2023: (Start) %F A035599 a(n) = 2*n*Hypergeometric2F1(1-n,1-k,2,2), where k=5. %F A035599 a(n) = A001847(n) - A001846(n). %F A035599 a(n) = A008413(n)*n/5. (End) %p A035599 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 %t A035599 CoefficientList[Series[2*x*(1+x)^4/(1-x)^6,{x,0,33}],x] (* _Vincenzo Librandi_, Apr 23 2012 *) %t A035599 LinearRecurrence[{6,-15,20,-15,6,-1},{0,2,20,102,360,1002},40] (* _Harvey P. Dale_, Dec 30 2023 *) %o A035599 (PARI) a(n)=(4*n^5+20*n^3+6*n)/15 \\ _Charles R Greathouse IV_, Dec 07 2011 %o A035599 (Magma) [(4*n^4+20*n^2+6)*n/15: n in [0..30]]; // _Vincenzo Librandi_, Apr 23 2012 %Y A035599 Cf. A035596-A035606. %Y A035599 Column 5 of A035607, A266213. Row 5 of A113413, A119800, A122542. %K A035599 nonn,easy %O A035599 0,2 %A A035599 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE