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Coordination sequence for 42-dimensional cubic lattice.
3

%I #35 Aug 27 2018 10:24:56

%S 1,84,3528,98812,2076816,34949796,490681688,5913144396,62456027424,

%T 587522034932,4985149915368,38549117382300,273998113272240,

%U 1803067831236420,11053262513080440,63460928860322028,342841481215636032

%N Coordination sequence for 42-dimensional cubic lattice.

%C First differs from A035806 at a(21). a(21)=721321863363711058916, whereas A035806(21)=721321867761757570020. - _Nathaniel Johnston_, Jun 26 2011

%H Seiichi Manyama, <a href="/A035737/b035737.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..500 from Nathaniel Johnston)

%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_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).

%H <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>

%F G.f.: ((1+x)/(1-x))^42.

%F n*a(n) = 84*a(n-1) + (n-2)*a(n-2) for n > 1. - _Seiichi Manyama_, Aug 27 2018

%p t:=taylor(((1+x)/(1-x))^42,x,30): seq(coeff(t,x,n),n=0..21); # _Nathaniel Johnston_, Jun 26 2011

%t CoefficientList[Series[((1+x)/(1-x))^42,{x,0,20}],x] (* _Harvey P. Dale_, Aug 03 2012 *)

%o (PARI) Vec((((1+x)/(1-x))^42) + O(x^17)) \\ _Felix Fröhlich_, Aug 27 2018

%K nonn,easy

%O 0,2

%A Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

%E Recomputed by _N. J. A. Sloane_, Nov 25 1998