A009925 Coordination sequence for CaF2(2), F position.

1, 4, 22, 24, 82, 64, 182, 124, 322, 204, 502, 304, 722, 424, 982, 564, 1282, 724, 1622, 904, 2002, 1104, 2422, 1324, 2882, 1564, 3382, 1824, 3922, 2104, 4502, 2404, 5122, 2724, 5782, 3064, 6482, 3424, 7222, 3804, 8002, 4204, 8822, 4624, 9682, 5064

Offset

0,2

References

Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (225) cF12.

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

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

G.f.: (1+4*x+19*x^2+12*x^3+19*x^4+4*x^5+x^6) / ((1-x)^3*(1+x)^3). - Colin Barker, Dec 12 2012

From Colin Barker, Jan 27 2016: (Start)

a(n) = (5*(-1)^n*n^2+15*n^2+(-1)^n+7)/4 for n>0.

a(n) = 5*n^2+2 for n>0 and even.

a(n) = (5*n^2+3)/2 for n odd.

(End)

Mathematica

CoefficientList[Series[-(x^6 + 4 x^5 + 19 x^4 + 12 x^3 + 19 x^2 + 4 x + 1)/((x - 1)^3 (x + 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Prog

(PARI) Vec((1+4*x+19*x^2+12*x^3+19*x^4+4*x^5+x^6)/((1-x)^3*(1+x)^3) + O(x^100)) \\ Colin Barker, Jan 27 2016

Crossrefs

Sequence in context: A268924 A185866 A043061 * A059653 A022385 A244411

Adjacent sequences: A009922 A009923 A009924 * A009926 A009927 A009928

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved