%I #17 Sep 05 2023 12:58:20
%S 1,84,3528,98812,2076816,34949796,490681688,5913144396,62456027424,
%T 587522034932,4985149915368,38549117382300,273998113272240,
%U 1803067831236420,11053262513080440,63460928860322028,342841481215636032,1750035197354015124
%N Coordination sequence for lattice D*_42 (with edges defined by l_1 norm = 1).
%C Starts to differ from A035737 at a(21). - _R. J. Mathar_, Oct 24 2008
%H Nathaniel Johnston, <a href="/A035806/b035806.txt">Table of n, a(n) for n = 0..500</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_42">Index entries for linear recurrences with constant coefficients</a>, signature (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).
%F a(n) = (Sum_{k=0..m} 2^k*binomial(m, k)*binomial(n-1, k-1)) + 2^m*binomial((m+2*n)/2-1, m-1), with m=42.
%p seq(add(2^k*binomial(42,k)*binomial(n-1,k-1),k=0..42) + 2^42*binomial((42+2*n)/2-1,41), n=0..21); # _Nathaniel Johnston_, Jun 26 2011
%K nonn
%O 0,2
%A _N. J. A. Sloane_, J. Serra-Sagrista (jserra(AT)ccd.uab.es)