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,-2,3,-3,2,-2,1).
FORMULA
For n > 1, a(n) = 2n^2 - 4n + 4 + p(n), with the 12-periodic sequence p(n) with period {0, 0, 0, -1, -1, 1, 0, -2, 0, 1, -1, -1}.
a(12*m+k) = 288*m^2 + 48*k*m + [ 2, 4, 9, 19, 35, 52, 72, 100, 131, 163, 201, 244 ], 0 <= k < 12. - N. J. A. Sloane
G.f.: -(x+1)^3*(x^4-x^3+3*x^2-x+1) / ((x-1)^3*(x^2+1)*(x^2+x+1)). - Colin Barker, Dec 12 2012
MATHEMATICA
CoefficientList[Series[-(x + 1)^3 (x^4 - x^3 + 3 x^2 - x + 1)/((x - 1)^3 (x^2 + 1) (x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved