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Coordination sequence T2 for Zeolite Code AWO.
1

%I #20 Apr 10 2018 08:26:36

%S 1,4,10,21,36,53,76,108,142,173,210,259,310,360,418,482,546,615,692,

%T 769,848,940,1036,1127,1224,1331,1438,1548,1672,1796,1912,2041,2184,

%U 2319,2452,2606,2766,2913,3068,3239,3404,3568,3754,3944,4118,4301,4504

%N Coordination sequence T2 for Zeolite Code AWO.

%C Also coordination sequence T3 for zeolite code UEI. - _Sean A. Irvine_, Mar 17 2018

%D W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.

%H R. W. Grosse-Kunstleve, <a href="/A038407/b038407.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 International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>

%F From _Colin Barker_, Feb 13 2018: (Start)

%F G.f.: (1 + x)*(1 + 3*x + 8*x^2 + 17*x^3 + 29*x^4 + 44*x^5 + 64*x^6 + 84*x^7 + 101*x^8 + 112*x^9 + 116*x^10 + 112*x^11 + 101*x^12 + 84*x^13 + 64*x^14 + 44*x^15 + 29*x^16 + 17*x^17 + 8*x^18 + 3*x^19 + x^20) / ((1 - x)^3*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2).

%F a(n) = -a(n-2) + a(n-5) + 3*a(n-7) + 2*a(n-9) - 2*a(n-12) - 3*a(n-14) - a(n-16) + a(n-19) + a(n-21) for n>21.

%F (End)

%K nonn

%O 0,2

%A _Ralf W. Grosse-Kunstleve_

%E Title improved by _Sean A. Irvine_, Mar 16 2018