A008014 Coordination sequence T1 for Zeolite Code AFI.

1, 4, 11, 21, 35, 53, 77, 105, 137, 172, 212, 256, 305, 357, 413, 473, 539, 609, 683, 760, 842, 928, 1019, 1113, 1211, 1313, 1421, 1533, 1649, 1768, 1892, 2020, 2153, 2289, 2429, 2573, 2723, 2877, 3035, 3196, 3362, 3532, 3707, 3885, 4067, 4253, 4445, 4641

Offset

0,2

References

W. M. Meier, D. H. Olson, and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.

Links

Vincenzo Librandi, 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.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).

Formula

a(10*m+k) = 210*m^2 + 42*k*m + one of 10 numbers depending on k, 0 <= k < 10. - N. J. A. Sloane

G.f.: -(x^2-x+1)*(x^2+x+1)*(x^8+2*x^7+3*x^6+x^5+x^3+3*x^2+2*x+1) / ((x-1)^3*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Dec 12 2012

Mathematica

CoefficientList[Series[-(x^2 - x + 1) (x^2 + x + 1) (x^8 + 2 x^7 + 3 x^6 + x^5 + x^3 + 3 x^2 + 2 x + 1)/((x - 1)^3 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Crossrefs

Sequence in context: A301111 A301235 A008008 * A008007 A307273 A009892

Adjacent sequences: A008011 A008012 A008013 * A008015 A008016 A008017

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved