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Coordination sequence T2 for feldspar.
1

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

%S 1,4,10,22,38,56,82,112,142,182,226,268,322,380,434,502,574,640,722,

%T 808,886,982,1082,1172,1282,1396,1498,1622,1750,1864,2002,2144,2270,

%U 2422,2578,2716,2882,3052,3202,3382,3566,3728,3922,4120,4294,4502,4714,4900

%N Coordination sequence T2 for feldspar.

%H Colin Barker, <a href="/A008255/b008255.txt">Table of n, a(n) for n = 0..1000</a>

%H R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</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+2, a(3*m+1) = 20*m^2+14*m+4, a(3*m+2) = 20*m^2+26*m+10.

%F G.f.: (1+x)^3*(1+3*x^2+x^4) / ((1-x)^3*(1+x+x^2)^2). - _Colin Barker_, Dec 22 2015

%t Table[SeriesCoefficient[(1 + x)^3 (1 + 3 x^2 + x^4)/((1 - x)^3 (1 + x + x^2)^2), {x, 0, n}], {n, 0, 47}] (* _Michael De Vlieger_, Dec 22 2015 *)

%t Join[{1}, LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {4, 10, 22, 38, 56, 82, 112}, 50]] (* _Vincenzo Librandi_, Dec 23 2015 *)

%o (PARI) Vec((1+x)^3*(1+3*x^2+x^4)/((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_