|
%I #16 Sep 07 2023 16:16:04
%S 1,0,3528,0,2076816,0,490681688,0,62456027424,0,4985149915368,0,
%T 273998113272240,0,11053262513080440,0,342841481215636032,0,
%U 8471578904288191496,0,171504713146698879696,2199023255552
%N Coordination sequence for diamond structure D^+_42. (Edges defined by l_1 norm = 1.)
%H Ray Chandler, <a href="/A035897/b035897.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 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_84">Index entries for linear recurrences with constant coefficients</a>, signature (0, 42, 0, -861, 0, 11480, 0, -111930, 0, 850668, 0, -5245786, 0, 26978328, 0, -118030185, 0, 445891810, 0, -1471442973, 0, 4280561376, 0, -11058116888, 0, 25518731280, 0, -52860229080, 0, 98672427616, 0, -166509721602, 0, 254661927156, 0, -353697121050, 0, 446775310800, 0, -513791607420, 0, 538257874440, 0, -513791607420, 0, 446775310800, 0, -353697121050, 0, 254661927156, 0, -166509721602, 0, 98672427616, 0, -52860229080, 0, 25518731280, 0, -11058116888, 0, 4280561376, 0, -1471442973, 0, 445891810, 0, -118030185, 0, 26978328, 0, -5245786, 0, 850668, 0, -111930, 0, 11480, 0, -861, 0, 42, 0, -1).
%p f := proc(m) local k,t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1,n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n,k)*binomial(m-1,k-1),k=0..n); fi; t1; end; where n=42.
%K nonn
%O 0,3
%A Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
%E Recomputed by _N. J. A. Sloane_, Nov 27 1998
|
