A008044 Coordination sequence T2 for Zeolite Code ATV.

1, 4, 12, 25, 42, 61, 88, 122, 160, 200, 246, 299, 358, 417, 480, 550, 628, 710, 796, 887, 984, 1083, 1188, 1298, 1412, 1530, 1656, 1789, 1926, 2063, 2206, 2356, 2512, 2670, 2832, 3001, 3178, 3357, 3540, 3728, 3922, 4120, 4324, 4533, 4746, 4961, 5184, 5414

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

a(40*m+k) = 3920*m^2 + 196*k*m + one of 40 numbers depending on k, 0<=k<40. - N. J. A. Sloane

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

G.f.: (1 + 3*x + 8*x^2 + 13*x^3 + 17*x^4 + 19*x^5 + 27*x^6 + 34*x^7 + 37*x^8 + 37*x^9 + 37*x^10 + 37*x^11 + 34*x^12 + 27*x^13 + 19*x^14 + 17*x^15 + 13*x^16 + 8*x^17 + 3*x^18 + x^19) / (1-x) / (1-x^8) / (1-x^10). - Sean A. Irvine, Mar 13 2018

Crossrefs

Sequence in context: A008073 A301049 A008097 * A008212 A008080 A008157

Adjacent sequences: A008041 A008042 A008043 * A008045 A008046 A008047

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved