A008259 Coordination sequence T2 for Moganite, also for BGB1.

1, 4, 11, 24, 41, 62, 90, 122, 157, 200, 247, 296, 354, 416, 479, 552, 629, 706, 794, 886, 977, 1080, 1187, 1292, 1410, 1532, 1651, 1784, 1921, 2054, 2202, 2354, 2501, 2664, 2831, 2992, 3170, 3352, 3527, 3720, 3917, 4106, 4314, 4526, 4729, 4952, 5179, 5396

Offset: 0

Author

Ralf W. Grosse-Kunstleve, David M. Teter (dmteter(AT)sandia.gov)

Keywords

• nonn
• easy

References

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..1000
• R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
• R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
• Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
• D. M. Teter, G.V. Gibbs, M. B. Boisen, D.C. Allan, and M. P. Teter, First principles study of several hypothetical silica framework structures, Physical Review B, 52 (1995), pp. 8064-8073.
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Programs

Mathematica

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

Formula

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

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