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Coordination sequence T2 for Moganite, also for BGB1.
2

%I #36 May 10 2024 22:16:51

%S 1,4,11,24,41,62,90,122,157,200,247,296,354,416,479,552,629,706,794,

%T 886,977,1080,1187,1292,1410,1532,1651,1784,1921,2054,2202,2354,2501,

%U 2664,2831,2992,3170,3352,3527,3720,3917,4106,4314,4526,4729,4952,5179,5396

%N Coordination sequence T2 for Moganite, also for BGB1.

%D Inorganic Crystal Structure Database: Collection Code 67669 (for Moganite)

%H Sean A. Irvine, <a href="/A008259/b008259.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 D. M. Teter, G.V. Gibbs, M. B. Boisen, D.C. Allan, and M. P. Teter, <a href="http://hdl.handle.net/10919/25375">First principles study of several hypothetical silica framework structures</a>, Physical Review B, 52 (1995), pp. 8064-8073.

%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) = 22m^2+2, a(3m+1) = 22m^2+15m+4, a(3m+2)=22m^2+29m+11. - _N. J. A. Sloane_

%F G.f.: -(x+1)*(x^6+2*x^5+5*x^4+6*x^3+5*x^2+2*x+1) / ((x-1)^3*(x^2+x+1)^2). - _Colin Barker_, Dec 12 2012

%t CoefficientList[Series[-(x + 1) (x^6 + 2 x^5 + 5 x^4 + 6 x^3 + 5 x^2 + 2 x + 1)/((x - 1)^3 (x^2 + x + 1)^2), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)

%t LinearRecurrence[{1,0,2,-2,0,-1,1},{1,4,11,24,41,62,90,122},70] (* _Harvey P. Dale_, May 10 2024 *)

%K nonn,easy

%O 0,2

%A _Ralf W. Grosse-Kunstleve_, David M. Teter (dmteter(AT)sandia.gov)