A008043 Coordination sequence T1 for Zeolite Code ATV.

1, 4, 11, 22, 40, 64, 92, 121, 157, 200, 248, 297, 351, 414, 484, 555, 630, 709, 795, 885, 980, 1081, 1187, 1297, 1414, 1535, 1660, 1786, 1919, 2061, 2208, 2356, 2509, 2669, 2836, 3004, 3176, 3354, 3539, 3728, 3922, 4120, 4323, 4530, 4744, 4964, 5188, 5413

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 + 5*x^2 + 6*x^3 + 12*x^4 + 12*x^5 + 16*x^6 + 13*x^7 + 22*x^8 + 18*x^9 + 22*x^10 + 13*x^11 + 16*x^12 + 12*x^13 + 12*x^14 + 6*x^15 + 5*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 18 2015

G.f.: (1 + 3*x + 7*x^2 + 11*x^3 + 18*x^4 + 24*x^5 + 28*x^6 + 29*x^7 + 35*x^8 + 40*x^9 + 40*x^10 + 35*x^11 + 29*x^12 + 28*x^13 + 24*x^14 + 18*x^15 + 11*x^16 + 7*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: A047951 A132072 A009846 * A088003 A049836 A177853

Adjacent sequences: A008040 A008041 A008042 * A008044 A008045 A008046

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved