A009926 Coordination sequence for CaF2(2), Ca position.

1, 8, 12, 48, 42, 128, 92, 248, 162, 408, 252, 608, 362, 848, 492, 1128, 642, 1448, 812, 1808, 1002, 2208, 1212, 2648, 1442, 3128, 1692, 3648, 1962, 4208, 2252, 4808, 2562, 5448, 2892, 6128, 3242, 6848, 3612, 7608, 4002, 8408, 4412, 9248, 4842

Offset

0,2

References

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

Links

Sean A. Irvine, 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

From Colin Barker, Sep 09 2014: (Start)

a(n) = (-2*(-5+(-1)^n)-5*(-3+(-1)^n)*n^2)/4 for n>0.

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6) for n>6.

G.f.: -(x^6+8*x^5+9*x^4+24*x^3+9*x^2+8*x+1) / ((x-1)^3*(x+1)^3). (End)

G.f.: (1+8*x+9*x^2+24*x^3+9*x^4+8*x^5+x^6) / (1-x^2)^3

Mathematica

Join[{1}, LinearRecurrence[{0, 3, 0, -3, 0, 1}, { 8, 12, 48, 42, 128, 92}, 44]] (* Georg Fischer, Feb 27 2019 *)

Crossrefs

Sequence in context: A032410 A077101 A229497 * A022668 A286360 A212815

Adjacent sequences: A009923 A009924 A009925 * A009927 A009928 A009929

Keyword

nonn

Author

Ralf W. Grosse-Kunstleve

Status

approved