A009946 Coordination sequence for NiAs(2), Ni position.

1, 6, 20, 42, 74, 114, 164, 222, 290, 366, 452, 546, 650, 762, 884, 1014, 1154, 1302, 1460, 1626, 1802, 1986, 2180, 2382, 2594, 2814, 3044, 3282, 3530, 3786, 4052, 4326, 4610, 4902, 5204, 5514, 5834, 6162, 6500, 6846, 7202, 7566, 7940, 8322, 8714

Offset

0,2

References

Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (194) hP4.

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

Reticular Chemistry Structure Resource, acs

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

a(0)=1, a(4n)=2*((6n)^2+1), a(4n+2)=18*(2n+1)^2+2, a(2n+1)=6*(3n^2+3n+1). - Ralf Stephan, Mar 07 2004

From Colin Barker, Aug 31 2013: (Start)

a(n) = (7+(-1)^n+18*n^2)/4 for n>0.

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4.

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

Mathematica

CoefficientList[Series[-(x^4 + 4 x^3 + 8 x^2 + 4 x + 1)/((x - 1)^3 (x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

Prog

(PARI) Vec(-(x^4+4*x^3+8*x^2+4*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Aug 31 2013

Crossrefs

Sequence in context: A077539 A068377 A002943 * A290154 A094274 A094279

Adjacent sequences: A009943 A009944 A009945 * A009947 A009948 A009949

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved