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Coordination sequence T1 for feldspar.
1

%I #23 Apr 10 2018 08:26:35

%S 1,4,10,20,38,58,80,112,144,180,226,270,320,380,436,500,574,642,720,

%T 808,888,980,1082,1174,1280,1396,1500,1620,1750,1866,2000,2144,2272,

%U 2420,2578,2718,2880,3052,3204,3380,3566,3730,3920,4120,4296,4500,4714,4902

%N Coordination sequence T1 for feldspar.

%D Inorganic Crystal Structure Database: Collection Code 100182.

%H Colin Barker, <a href="/A008254/b008254.txt">Table of n, a(n) for n = 0..1000</a>

%H R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, <a href="http://neilsloane.com/doc/ac96cs/">Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites</a>, Acta Cryst., A52 (1996), pp. 879-889.

%H Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).

%F 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).

%F 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

%t 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 *)

%o (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

%K nonn,easy

%O 0,2

%A Georg Thimm (mgeorg(AT)ntu.edu.sg) and _Ralf W. Grosse-Kunstleve_