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A009946 Coordination sequence for NiAs(2), Ni position. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A002943 A068377 * A290154 A094274 A094279

Adjacent sequences:  A009943 A009944 A009945 * A009947 A009948 A009949

KEYWORD

nonn,easy

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

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Last modified November 18 09:23 EST 2018. Contains 317279 sequences. (Running on oeis4.)