A008228 - OEIS

%I #22 Apr 10 2018 08:26:35

%S 1,4,9,18,32,48,68,96,126,155,191,234,277,322,373,429,490,555,620,688,

%T 765,845,923,1007,1099,1192,1289,1395,1500,1602,1716,1838,1954,2073,

%U 2203,2336,2473,2617,2757,2897,3053,3212,3362,3521,3692,3861,4035,4220

%N Coordination sequence T2 for Zeolite Code PHI.

%C Also coordination sequence T3 for zeolite code SIV. - _Sean A. Irvine_, Mar 19 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="/A008228/b008228.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 G.f.: (1 + x) * (1 + x + 4*x^2 + 5*x^3 + 9*x^4 + 10*x^5 + 16*x^6 + 16*x^7 + 22*x^8 + 21*x^9 + 26*x^10 + 24*x^11 + 26*x^12 + 21*x^13 + 22*x^14 + 16*x^15 + 16*x^16 + 10*x^17 + 9*x^18 + 5*x^19 + 4*x^20 + x^21 + x^22) / ((1 - x)^3 * (1 + x^2) * (1 + x + x^2) * (1 - x + x^2 - x^3 + x^4)^2 * (1 + x + x^2 + x^3 + x^4)^2). - _Colin Barker_, Dec 20 2015

%F G.f.: (1 + 4*x + 35*x^5 + 41*x^6 + 47*x^7 + 9*x^2 + 17*x^3 + 27*x^4 + 50*x^8 + 48*x^9 + 43*x^10 + 36*x^11 + 26*x^12 + 10*x^13 - 10*x^14 - 26*x^15 - 36*x^16 - 43*x^17 - 48*x^18 - 50*x^19 - 47*x^20 - 41*x^21 - 35*x^22 - 27*x^23 - 17*x^24 - 9*x^25 - 4*x^26 - x^27) / (1 - x^3) / (1 - x^4) / (1 - x^10)^2. - _Sean A. Irvine_, Mar 14 2018

%K nonn

%O 0,2

%A _Ralf W. Grosse-Kunstleve_