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, and 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.

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

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

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

From Jianing Song, May 22 2026: (Start)

a(n) = a(n-2) + 2*a(n-3) + a(n-4) + 2*a(n-5) - 2*a(n-7) - a(n-8) - 2*a(n-9) + a(n-10) + a(n-12) for n >= 15.

a(n) = (187*n^2 + c1*n + c0)/12 for n >= 3, where c1 = [-72,-86,-100,-54,-104,-118,-36,-86,-136,-54,-68,-118] and c0 = [-216,139,196,-81,40,43,36,175,-56,-117,292,79] for n == 0..11 (mod 12). (End)

Prog

(PARI) a(n) = if(n<=2, [1, 12, 50][n+1], my(c1=[-72, -86, -100, -54, -104, -118, -36, -86, -136, -54, -68, -118], c0 = [-216, 139, 196, -81, 40, 43, 36, 175, -56, -117, 292, 79]); (187*n^2 + c1[n%12+1]*n + c0[n%12+1])/12) \\ Jianing Song, May 22 2026

Crossrefs

Sequence in context: A066644 A009934 A396527 * A009938 A063491 A248230

Adjacent sequences: A009924 A009925 A009926 * A009928 A009929 A009930

Keyword

nonn,easy

Author

Ralf W. Grosse-Kunstleve

Status

approved