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

0,2

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

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

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 *)

Crossrefs

Sequence in context: A362072 A102533 A341133 * A047954 A008144 A289388

Adjacent sequences: A008030 A008031 A008032 * A008034 A008035 A008036

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved