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Coordination sequence T1 for Zeolite Code JBW.
1

%I #23 Dec 22 2022 14:39:46

%S 1,4,10,21,39,61,81,107,148,192,228,266,324,393,449,503,575,659,738,

%T 814,906,1002,1090,1191,1311,1427,1521,1629,1780,1926,2036,2148,2308,

%U 2487,2625,2753,2919,3105,3274,3432,3618,3808,3978,4169,4391,4601,4769,4959

%N Coordination sequence T1 for Zeolite Code JBW.

%H R. W. Grosse-Kunstleve, <a href="/A008121/b008121.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 International Zeolite Association, <a href="http://www.iza-structure.org/databases/">Database of Zeolite Structures</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,-2,2,-1,3,-2,4,-4,2,-3,1,-2,2,-1,1).

%F G.f.: (1 + x) * (1 - x + x^2) * (1 + 3*x + 8*x^2 + 16*x^3 + 28*x^4 + 37*x^5 + 40*x^6 + 37*x^7 + 28*x^8 + 16*x^9 + 8*x^10 + 3*x^11 + x^12) / ((1 - x)^3 * (1 + x^2)^2 * (1 + x + x^2 + x^3 + x^4)^2). - _Colin Barker_, Dec 18 2015

%t CoefficientList[Series[(1 + x) * (1 - x + x^2) * (1 + 3*x + 8*x^2 + 16*x^3 + 28*x^4 + 37*x^5 + 40*x^6 + 37*x^7 + 28*x^8 + 16*x^9 + 8*x^10 + 3*x^11 + x^12) / ((1 - x)^3 * (1 + x^2)^2 * (1 + x + x^2 + x^3 + x^4)^2),{x,0,47}],x] (* _Stefano Spezia_, Dec 22 2022 *)

%Y Cf. A005897, A008000.

%K nonn,easy

%O 0,2

%A _Ralf W. Grosse-Kunstleve_