%I #49 Nov 20 2022 12:06:09
%S 1,4,10,21,36,54,78,106,136,173,214,256,306,360,414,477,544,610,686,
%T 766,844,933,1026,1116,1218,1324,1426,1541,1660,1774,1902,2034,2160,
%U 2301,2446,2584,2738,2896,3046,3213,3384,3546,3726,3910,4084,4277,4474,4660
%N Coordination sequence T1 for Zeolite Code ABW and ATN.
%D W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996
%H Vincenzo Librandi, <a href="/A008000/b008000.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 International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>
%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 <a href="/index/Con#coordseqs">Index entries for Coordination Sequences</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F a(3m)=19m^2+2, a(3m+1)=19m^2+13m+4, a(3m+2)=19m^2+25m+10, for m>0. [_N. J. A. Sloane_]
%F G.f.: (1+3*x+6*x^2+9*x^3+9*x^4+6*x^5+3*x^6+x^7)/((1-x)^3*(1+x+x^2)^2). [_Vladimir Joseph Stephan Orlovsky_]
%t CoefficientList[Series[(-z^7 - 3 z^6 - 6 z^5 - 9 z^4 - 9 z^3 - 6 z^2 - 3 z - 1)/((z - 1)^3 (z^2 + z + 1)^2), {z, 0, 100}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)
%o (PARI) a(n)=if(n,my(m=divrem(n,3));19*m[1]^2+if(m[2],if(m[2]==1,13*m[1]+4,25*m[1]+10),2),1) \\ _Charles R Greathouse IV_, Jun 28 2011
%o (Magma) I:=[1,4,10,21,36,54,78,106]; [n le 8 select I[n] else Self(n-1)+2*Self(n-3)-2*Self(n-4)-Self(n-6)+Self(n-7): n in [1..50]]; // _Vincenzo Librandi_, Jun 10 2013
%K nonn,easy
%O 0,2
%A _Ralf W. Grosse-Kunstleve_