A038407 Coordination sequence T2 for Zeolite Code AWO.

1, 4, 10, 21, 36, 53, 76, 108, 142, 173, 210, 259, 310, 360, 418, 482, 546, 615, 692, 769, 848, 940, 1036, 1127, 1224, 1331, 1438, 1548, 1672, 1796, 1912, 2041, 2184, 2319, 2452, 2606, 2766, 2913, 3068, 3239, 3404, 3568, 3754, 3944, 4118, 4301, 4504

Offset

0,2

Comments

Also coordination sequence T3 for zeolite code UEI. - Sean A. Irvine, Mar 17 2018

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

From Colin Barker, Feb 13 2018: (Start)

G.f.: (1 + x)*(1 + 3*x + 8*x^2 + 17*x^3 + 29*x^4 + 44*x^5 + 64*x^6 + 84*x^7 + 101*x^8 + 112*x^9 + 116*x^10 + 112*x^11 + 101*x^12 + 84*x^13 + 64*x^14 + 44*x^15 + 29*x^16 + 17*x^17 + 8*x^18 + 3*x^19 + x^20) / ((1 - x)^3*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2).

a(n) = -a(n-2) + a(n-5) + 3*a(n-7) + 2*a(n-9) - 2*a(n-12) - 3*a(n-14) - a(n-16) + a(n-19) + a(n-21) for n>21.

(End)

Crossrefs

Sequence in context: A373187 A363607 A008145 * A301012 A009894 A301013

Adjacent sequences: A038404 A038405 A038406 * A038408 A038409 A038410

Keyword

nonn

Author

Ralf W. Grosse-Kunstleve

Extensions

Title improved by Sean A. Irvine, Mar 16 2018

Status

approved