%I #36 Sep 08 2022 08:44:52
%S 1,68,2312,52428,892432,12168532,138504984,1354168796,11614313504,
%T 88805833316,613171117352,3863171679980,22402282117680,
%U 120450005575540,604244840324920,2843633280971772,12614155679414336,52965710906750084,211305268473868616
%N Coordination sequence for 34-dimensional cubic lattice.
%H Seiichi Manyama, <a href="/A035729/b035729.txt">Table of n, a(n) for n = 0..10000</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="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_34">Index entries for linear recurrences with constant coefficients</a>, signature (34, -561, 5984, -46376, 278256, -1344904, 5379616, -18156204, 52451256, -131128140, 286097760, -548354040, 927983760, -1391975640, 1855967520, -2203961430, 2333606220, -2203961430, 1855967520, -1391975640, 927983760, -548354040, 286097760, -131128140, 52451256, -18156204, 5379616, -1344904, 278256, -46376, 5984, -561, 34, -1).
%F G.f.: ((1+x)/(1-x))^34. [clarified by _Harvey P. Dale_, Dec 07 2014]
%F n*a(n) = 68*a(n-1) + (n-2)*a(n-2) for n > 1. - _Seiichi Manyama_, Aug 24 2018
%p seq(coeff(series(((1+x)/(1-x))^34, x, n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Aug 24 2018
%t CoefficientList[Series[((1+x)/(1-x))^34,{x,0,20}],x] (* _Harvey P. Dale_, Dec 07 2014 *)
%o (GAP) a:=[1,68];; for n in [3..20] do a[n]:=1/(n-1)*(68*a[n-1]+(n-3)*a[n-2]); od; a; # _Muniru A Asiru_, Aug 24 2018
%o (PARI) x='x+O('x^25); Vec(((1+x)/(1-x))^34) \\ _Altug Alkan_, Aug 24 2018
%o (Magma) I:=[1,68]; [n le 2 select I[n] else 1/(n-1)*(68*Self(n-1)+(n-3)*Self(n-2)): n in [1..30]]; // _Vincenzo Librandi_, Aug 29 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