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%I #22 Sep 05 2023 12:56:49
%S 1,20,200,1340,6800,29028,108120,355980,1047840,2793140,6830056,
%T 15502300,32993200,66410500,127335800,233975084,414071360,708767060,
%U 1177632520,1905107580,3008636112,4648808100,7041860760,10474929100,15324477280,22078385140,31362209320
%N Coordination sequence for lattice D*_10 (with edges defined by l_1 norm = 1).
%H Vincenzo Librandi, <a href="/A035474/b035474.txt">Table of n, a(n) for n = 0..1000</a>
%H Joan Serra-Sagrista, <a href="http://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_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
%F a(m) = sum(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1), where n=10, a(0)=1.
%F G.f.: (x^2+6*x+1)*(x^8+4*x^7+20*x^6-4*x^5+214*x^4-4*x^3+20*x^2+4*x+1) / (x-1)^10. [_Colin Barker_, Nov 19 2012]
%t CoefficientList[Series[(x^2 + 6 x + 1) (x^8 + 4 x^7 + 20 x^6 - 4 x^5 + 214 x^4 - 4 x^3 + 20 x^2 + 4 x + 1)/(x - 1)^10, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,20,200,1340,6800,29028,108120,355980,1047840,2793140,6830056},30] (* _Harvey P. Dale_, Mar 22 2020 *)
%o (Magma) n:=10; [1] cat [&+[2^k*Binomial(n, k)*Binomial(m-1, k-1): k in [0..n]]+2^n*Binomial((n+2*m) div 2-1, n-1): m in [1..30]]; // _Bruno Berselli_, Oct 21 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
%E More terms from _Vincenzo Librandi_, Oct 21 2013
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