A008261 Coordination sequence for quartz.

1, 4, 12, 30, 52, 80, 116, 156, 204, 258, 318, 384, 458, 536, 622, 714, 812, 916, 1028, 1144, 1268, 1398, 1534, 1676, 1826, 1980, 2142, 2310, 2484, 2664, 2852, 3044, 3244, 3450, 3662, 3880, 4106, 4336, 4574, 4818, 5068, 5324, 5588, 5856, 6132, 6414, 6702

Offset

0,2

References

Inorganic Crystal Structure Database: Collection Code 31048.

Links

Sean A. Irvine, Table of n, a(n) for n = 0..1000

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

Formula

a(6m)=114m^2+2, a(6m+1)=114m^2+38m+4, a(6m+2)=114m^2+76m+14 (m>0), a(6m+3)=114m^2+114m+30, a(6m+4)=114m^2+152m+52, a(6m+5)=114m^2+190m+80 (N. J. A. Sloane).

Maple

(1+3*x+7*x^2+14*x^3+11*x^4+3*x^5-x^6-2*x^7+2*x^8)/(1-x^3)/(1-x^2)/(1-x);

Crossrefs

Sequence in context: A280007 A061726 A067706 * A099407 A011938 A047177

Adjacent sequences: A008258 A008259 A008260 * A008262 A008263 A008264

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved