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

0,2

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.

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).

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]

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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A009894 A301013 A027370 * A038408 A038411 A033599

Adjacent sequences: A007997 A007998 A007999 * A008001 A008002 A008003

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved