%I #38 Apr 10 2018 08:26:36
%S 1,6,20,42,74,114,164,222,290,366,452,546,650,762,884,1014,1154,1302,
%T 1460,1626,1802,1986,2180,2382,2594,2814,3044,3282,3530,3786,4052,
%U 4326,4610,4902,5204,5514,5834,6162,6500,6846,7202,7566,7940,8322,8714
%N Coordination sequence for NiAs(2), Ni position.
%D Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (194) hP4.
%H Vincenzo Librandi, <a href="/A009946/b009946.txt">Table of n, a(n) for n = 0..1000</a>
%H R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</a>
%H R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, <a href="http://neilsloane.com/doc/ac96cs/">Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites</a>, Acta Cryst., A52 (1996), pp. 879-889.
%H Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>
%H Reticular Chemistry Structure Resource, <a href="http://rcsr.anu.edu.au/nets/acs">acs</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(0)=1, a(4n)=2*((6n)^2+1), a(4n+2)=18*(2n+1)^2+2, a(2n+1)=6*(3n^2+3n+1). - _Ralf Stephan_, Mar 07 2004
%F From _Colin Barker_, Aug 31 2013: (Start)
%F a(n) = (7+(-1)^n+18*n^2)/4 for n>0.
%F a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4.
%F G.f.: -(x^4+4*x^3+8*x^2+4*x+1) / ((x-1)^3*(x+1)). (End)
%t CoefficientList[Series[-(x^4 + 4 x^3 + 8 x^2 + 4 x + 1)/((x - 1)^3 (x + 1)),{x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%o (PARI) Vec(-(x^4+4*x^3+8*x^2+4*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Aug 31 2013
%K nonn,easy
%O 0,2
%A _Ralf W. Grosse-Kunstleve_