A008000 Coordination sequence T1 for Zeolite Code ABW and ATN.

1, 4, 10, 21, 36, 54, 78, 106, 136, 173, 214, 256, 306, 360, 414, 477, 544, 610, 686, 766, 844, 933, 1026, 1116, 1218, 1324, 1426, 1541, 1660, 1774, 1902, 2034, 2160, 2301, 2446, 2584, 2738, 2896, 3046, 3213, 3384, 3546, 3726, 3910, 4084, 4277, 4474, 4660

Offset: 0

Author

Ralf W. Grosse-Kunstleve

Keywords

• nonn
• easy

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.
• International Zeolite Association, Database of Zeolite Structures
• Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
• Index entries for Coordination Sequences.
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Programs

Magma

I:=[1,4,10,21,36,54,78,106]; [n le 8 select I[n] else Self(n-1)+2*Self(n-3)-2*Self(n-4)-Self(n-6)+Self(n-7): n in [1..50]]; // Vincenzo Librandi, Jun 10 2013

Mathematica

CoefficientList[Series[(-z^7 - 3 z^6 - 6 z^5 - 9 z^4 - 9 z^3 - 6 z^2 - 3 z - 1)/((z - 1)^3 (z^2 + z + 1)^2), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 27 2011 *)

PARI

a(n)=if(n,my(m=divrem(n,3));19*m[1]^2+if(m[2],if(m[2]==1,13*m[1]+4,25*m[1]+10),2),1) \\ Charles R Greathouse IV, Jun 28 2011

Formula

a(3m)=19m^2+2, a(3m+1)=19m^2+13m+4, a(3m+2)=19m^2+25m+10, for m>0. [N. J. A. Sloane]

G.f.: (1+3*x+6*x^2+9*x^3+9*x^4+6*x^5+3*x^6+x^7)/((1-x)^3*(1+x+x^2)^2). [Vladimir Joseph Stephan Orlovsky]