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A008014 Coordination sequence T1 for Zeolite Code AFI.

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%I A008014 #36 Feb 07 2024 09:00:11
%S A008014 1,4,11,21,35,53,77,105,137,172,212,256,305,357,413,473,539,609,683,
%T A008014 760,842,928,1019,1113,1211,1313,1421,1533,1649,1768,1892,2020,2153,
%U A008014 2289,2429,2573,2723,2877,3035,3196,3362,3532,3707,3885,4067,4253,4445,4641
%N A008014 Coordination sequence T1 for Zeolite Code AFI.
%D A008014 W. M. Meier, D. H. Olson, and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.
%H A008014 Vincenzo Librandi, <a href="/A008014/b008014.txt">Table of n, a(n) for n = 0..1000</a>
%H A008014 R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</a>.
%H A008014 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 A008014 Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>.
%H A008014 International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>.
%H A008014 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).
%F A008014 a(10*m+k) = 210*m^2 + 42*k*m + one of 10 numbers depending on k, 0 <= k < 10. - _N. J. A. Sloane_
%F A008014 G.f.: -(x^2-x+1)*(x^2+x+1)*(x^8+2*x^7+3*x^6+x^5+x^3+3*x^2+2*x+1) / ((x-1)^3*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Dec 12 2012
%t A008014 CoefficientList[Series[-(x^2 - x + 1) (x^2 + x + 1) (x^8 + 2 x^7 + 3 x^6 + x^5 + x^3 + 3 x^2 + 2 x + 1)/((x - 1)^3 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%K A008014 nonn,easy
%O A008014 0,2
%A A008014 _Ralf W. Grosse-Kunstleve_