A008033 Coordination sequence T2 for Zeolite Code APC.

1, 4, 10, 20, 35, 54, 76, 104, 136, 171, 211, 254, 302, 355, 411, 471, 536, 606, 679, 756, 837, 922, 1013, 1107, 1204, 1307, 1414, 1525, 1640, 1758, 1881, 2009, 2141, 2276, 2416, 2561, 2709, 2862, 3018, 3178, 3344, 3513, 3686, 3864, 4046, 4232, 4422, 4616

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

• R. W. Grosse-Kunstleve, 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

Programs

Mathematica

CoefficientList[Series[(1 + 3*x + 6*x^2 + 10*x^3 + 15*x^4 + 18*x^5 + 19*x^6 + 22*x^7 + 22*x^8 + 19*x^9 + 18*x^10 + 15*x^11 + 10*x^12 + 6*x^13 + 3*x^14 + x^15)/(1-x)/(1-x^5)/(1-x^9),{x,0,47}],x] (* Stefano Spezia, Dec 17 2022 *)

Formula

G.f.: (1 + x)*(1 + 2*x + 4*x^2 + 6*x^3 + 9*x^4 + 9*x^5 + 10*x^6 + 12*x^7 + 10*x^8 + 9*x^9 + 9*x^10 + 6*x^11 + 4*x^12 + 2*x^13 + x^14) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x^3 + x^6)). - Colin Barker, Dec 20 2015

G.f.: (1 + 3*x + 6*x^2 + 10*x^3 + 15*x^4 + 18*x^5 + 19*x^6 + 22*x^7 + 22*x^8 + 19*x^9 + 18*x^10 + 15*x^11 + 10*x^12 + 6*x^13 + 3*x^14 + x^15) / (1 - x) / (1 - x^5) / (1 - x^9). - Sean A. Irvine, Mar 13 2018

a(n) ~ 94*n^2/45. - Stefano Spezia, Dec 17 2022