A008228 Coordination sequence T2 for Zeolite Code PHI.

1, 4, 9, 18, 32, 48, 68, 96, 126, 155, 191, 234, 277, 322, 373, 429, 490, 555, 620, 688, 765, 845, 923, 1007, 1099, 1192, 1289, 1395, 1500, 1602, 1716, 1838, 1954, 2073, 2203, 2336, 2473, 2617, 2757, 2897, 3053, 3212, 3362, 3521, 3692, 3861, 4035, 4220

Offset

0,2

Comments

Also coordination sequence T3 for zeolite code SIV. - Sean A. Irvine, Mar 19 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

G.f.: (1 + x) * (1 + x + 4*x^2 + 5*x^3 + 9*x^4 + 10*x^5 + 16*x^6 + 16*x^7 + 22*x^8 + 21*x^9 + 26*x^10 + 24*x^11 + 26*x^12 + 21*x^13 + 22*x^14 + 16*x^15 + 16*x^16 + 10*x^17 + 9*x^18 + 5*x^19 + 4*x^20 + x^21 + x^22) / ((1 - x)^3 * (1 + x^2) * (1 + x + x^2) * (1 - x + x^2 - x^3 + x^4)^2 * (1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 20 2015

G.f.: (1 + 4*x + 35*x^5 + 41*x^6 + 47*x^7 + 9*x^2 + 17*x^3 + 27*x^4 + 50*x^8 + 48*x^9 + 43*x^10 + 36*x^11 + 26*x^12 + 10*x^13 - 10*x^14 - 26*x^15 - 36*x^16 - 43*x^17 - 48*x^18 - 50*x^19 - 47*x^20 - 41*x^21 - 35*x^22 - 27*x^23 - 17*x^24 - 9*x^25 - 4*x^26 - x^27) / (1 - x^3) / (1 - x^4) / (1 - x^10)^2. - Sean A. Irvine, Mar 14 2018

Crossrefs

Sequence in context: A008266 A301200 A008222 * A008160 A301201 A301199

Adjacent sequences: A008225 A008226 A008227 * A008229 A008230 A008231

Keyword

nonn

Author

Ralf W. Grosse-Kunstleve

Status

approved