A008013 Coordination sequence occurring in Zeolite Codes AFG, CAN, LIO, LOS.

1, 4, 10, 20, 34, 54, 78, 104, 134, 168, 210, 256, 302, 352, 406, 470, 538, 604, 674, 748, 834, 924, 1010, 1100, 1194, 1302, 1414, 1520, 1630, 1744, 1874, 2008, 2134, 2264, 2398, 2550, 2706, 2852, 3002, 3156, 3330, 3508, 3674, 3844, 4018, 4214, 4414, 4600

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 (1,0,0,0,2,-2,0,0,0,-1,1).

Formula

a(5m)=52*m^2+2, a(5m+1)=52*m^2+22*m+4, a(5m+2)=52*m^2+42*m+10, a(5m+3)=52*m^2+62*m+20, a(5m+4)=52*m^2+82*m+34. - N. J. A. Sloane

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

Mathematica

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

Crossrefs

Sequence in context: A301029 A301122 A301038 * A301154 A024991 A000742

Adjacent sequences: A008010 A008011 A008012 * A008014 A008015 A008016

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved