A009927 Coordination sequence for Cr3Si, Si position.

1, 12, 50, 120, 218, 344, 546, 728, 902, 1212, 1526, 1784, 2154, 2552, 2954, 3432, 3854, 4340, 4998, 5504, 6002, 6768, 7442, 8024, 8814, 9572, 10334, 11232, 11978, 12824, 13938, 14768, 15590, 16812, 17846, 18752, 19962, 21080, 22202, 23520

Offset

0,2

References

Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (223) cP8.

Links

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000

V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586. See Table I.

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.

Formula

G.f.: (1+12*x+51*x^2+130*x^3+243*x^4+350*x^5+450*x^6+418*x^7 +327*x^8+182*x^9+51*x^10+16*x^11-7*x^12+8*x^13+12*x^14)/ ((1+x)*(1+x^2)^2*(1+x+x^2)^2*(1-x)^3). - Robert Israel, Dec 18 2015

Empirical: a(n) = (1903/72) + (3/8)*(-1)^n + 19*KroneckerDelta[n,0] - 8*KroneckerDelta[n,1] - 12*KroneckerDelta[n,2] + ((n+1)/12)*(187*n-273) - (32*sqrt(3)/27)*((13/2)*cos((4n+1)*Pi/6) + sin(2n*Pi/3)) - (3*sqrt(26)/2)*(-1)^n*cos(n*Pi/2 + arctan(1/5)) - (3/4)*i^n*(1+(-1)^n)*(n+2). - G. C. Greubel, Dec 18 2015

G.f.: (1 + 12*x + 50*x^2 + 118*x^3 + 192*x^4 + 220*x^5 + 207*x^6 + 68*x^7-123*x^8-236*x^9-276*x^10-166*x^11-58*x^12-8*x^13 + 19*x^14-8*x^15-12*x^16) / (1-x^3)^2 / (1-x^4)^2. - Sean A. Irvine, Mar 15 2018

Crossrefs

Sequence in context: A009930 A066644 A009934 * A009938 A063491 A248230

Adjacent sequences: A009924 A009925 A009926 * A009928 A009929 A009930

Keyword

nonn

Author

Ralf W. Grosse-Kunstleve

Status

approved