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%I #41 Sep 08 2022 08:44:52
%S 0,2,44,486,3608,20330,93060,361550,1229360,3742290,10377180,26572086,
%T 63521352,143027898,305568564,623207070,1219605600,2300164770,
%U 4196289420,7428962950,12798246520,21507034122
%N Number of points of L1 norm 11 in cubic lattice Z^n.
%H Vincenzo Librandi, <a href="/A035605/b035605.txt">Table of n, a(n) for n = 0..1000</a>
%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - _N. J. A. Sloane_, Feb 13 2013
%H M. Janjic, B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5.
%H Joan Serra-Sagrista, <a href="https://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F From _Colin Barker_, Apr 15 2012: (Start)
%F a(n) = (2*n*(14175 + 83754*n^2 + 50270*n^4 + 7392*n^6 + 330*n^8 + 4*n^10))/155925.
%F G.f.: 2*x*(1+x)^10/(1-x)^12. (End)
%p 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 CoefficientList[Series[2*x*(1+x)^10/(1-x)^12,{x,0,30}],x] (* _Vincenzo Librandi_, Apr 24 2012 *)
%t LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{0,2,44,486,3608,20330,93060,361550,1229360,3742290,10377180,26572086},30] (* _Harvey P. Dale_, Dec 23 2016 *)
%o (Magma) [(2*n*(14175+83754*n^2+50270*n^4+7392*n^6+330*n^8+ 4*n^10))/155925: n in [0..30]]; /* or */
%o I:=[0, 2, 44, 486, 3608, 20330, 93060, 361550, 1229360, 3742290, 10377180, 26572086]; [n le 12 select I[n] else 12*Self(n-1)-66*Self(n-2)+220*Self(n-3)-495*Self(n-4)+792*Self(n-5)-924*Self(n-6)+792*Self(n-7)-495*Self(n-8)+220*Self(n-9)-66*Self(n-10)+12*Self(n-11)-Self(n-12): n in [1..31]]; // _Vincenzo Librandi_, Apr 24 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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