A008254 Coordination sequence T1 for feldspar.

1, 4, 10, 20, 38, 58, 80, 112, 144, 180, 226, 270, 320, 380, 436, 500, 574, 642, 720, 808, 888, 980, 1082, 1174, 1280, 1396, 1500, 1620, 1750, 1866, 2000, 2144, 2272, 2420, 2578, 2718, 2880, 3052, 3204, 3380, 3566, 3730, 3920, 4120, 4296, 4500, 4714, 4902

Offset

0,2

References

Inorganic Crystal Structure Database: Collection Code 100182.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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 (1,0,2,-2,0,-1,1).

Formula

a(3*m) = 20*m^2, a(3*m+1) = 20*m^2+14*m+4, a(3*m+2) = 20*m^2+26*m+12 (m>0).

G.f.: (1+x)*(1+2*x+4*x^2+4*x^3+8*x^4+3*x^6-4*x^7+2*x^8) / ((1-x)^3*(1+x+x^2)^2). - Colin Barker, Dec 22 2015

Mathematica

Table[SeriesCoefficient[(1 + x) (1 + 2 x + 4 x^2 + 4 x^3 + 8 x^4 + 3 x^6 - 4 x^7 + 2 x^8)/((1 - x)^3 (1 + x + x^2)^2), {x, 0, n}], {n, 0, 47}] (* Michael De Vlieger, Dec 22 2015 *)

Prog

(PARI) Vec((1+x)*(1+2*x+4*x^2+4*x^3+8*x^4+3*x^6-4*x^7+2*x^8)/((1-x)^3*(1+x+x^2)^2) + O(x^100)) \\ Colin Barker, Dec 22 2015

Crossrefs

Sequence in context: A188280 A295950 A038420 * A301178 A279262 A168673

Adjacent sequences: A008251 A008252 A008253 * A008255 A008256 A008257

Keyword

nonn,easy

Author

Georg Thimm (mgeorg(AT)ntu.edu.sg) and Ralf W. Grosse-Kunstleve

Status

approved