A008084 Coordination sequence T1 for Zeolite Code ACO, ASV, EDI, and THO.

1, 4, 9, 19, 35, 52, 72, 100, 131, 163, 201, 244, 290, 340, 393, 451, 515, 580, 648, 724, 803, 883, 969, 1060, 1154, 1252, 1353, 1459, 1571, 1684, 1800, 1924, 2051, 2179, 2313, 2452, 2594, 2740, 2889, 3043, 3203, 3364, 3528, 3700, 3875, 4051, 4233, 4420

Offset: 0

Author

Ralf W. Grosse-Kunstleve

Keywords

• nonn
• easy

References

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

Links

• Vincenzo Librandi, 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.
• International Zeolite Association, Database of Zeolite Structures.
• Reticular Chemistry Structure Resource, nets pcb, pcb-b, asv, edi, edi-c.
• Index entries for linear recurrences with constant coefficients, signature (2,-2,3,-3,2,-2,1).

Programs

Mathematica

CoefficientList[Series[-(x + 1)^3 (x^4 - x^3 + 3 x^2 - x + 1)/((x - 1)^3 (x^2 + 1) (x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Formula

For n > 1, a(n) = 2n^2 - 4n + 4 + p(n), with the 12-periodic sequence p(n) with period {0, 0, 0, -1, -1, 1, 0, -2, 0, 1, -1, -1}.

a(12*m+k) = 288*m^2 + 48*k*m + [ 2, 4, 9, 19, 35, 52, 72, 100, 131, 163, 201, 244 ], 0 <= k < 12. - N. J. A. Sloane

G.f.: -(x+1)^3*(x^4-x^3+3*x^2-x+1) / ((x-1)^3*(x^2+1)*(x^2+x+1)). - Colin Barker, Dec 12 2012