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 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved