A009924 Coordination sequence for CaF2(1), F position.

1, 10, 34, 82, 142, 218, 322, 434, 562, 722, 886, 1066, 1282, 1498, 1730, 2002, 2270, 2554, 2882, 3202, 3538, 3922, 4294, 4682, 5122, 5546, 5986, 6482, 6958, 7450, 8002, 8530, 9074, 9682, 10262, 10858, 11522, 12154, 12802, 13522, 14206, 14906

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 (1,0,2,-2,0,-1,1).

Formula

G.f.: -(x^3+4*x^2+2*x+1)*(x^4+5*x^3+6*x^2+7*x+1) / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Dec 12 2012

a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7). - Wesley Ivan Hurt, Mar 17 2023

Mathematica

CoefficientList[Series[-(x^3 + 4 x^2 + 2 x + 1) (x^4 + 5 x^3 + 6 x^2 + 7 x + 1)/((x - 1)^3 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Crossrefs

Sequence in context: A366415 A007584 A218329 * A297721 A019257 A288782

Adjacent sequences: A009921 A009922 A009923 * A009925 A009926 A009927

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved