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%I #40 Aug 05 2022 07:46:16
%S 1,4,9,17,28,41,56,73,93,117,146,180,216,253,291,329,369,414,466,524,
%T 586,650,712,773,836,902,973,1051,1136,1224,1313,1403,1492,1581,1673,
%U 1769,1870,1978,2093,2211,2329,2447,2563,2678,2797,2923,3057,3198,3344
%N Coordination sequence T2 for Zeolite Code TSC.
%C First 127 terms computed by _Davide M. Proserpio_ using ToposPro.
%H R. W. Grosse-Kunstleve, <a href="/A033617/b033617.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..127 from Davide M. Proserpio)
%H V. A. Blatov, A. P. Shevchenko, and D. M. Proserpio, <a href="https://doi.org/10.1021/cg500498k">Applied Topological Analysis of Crystal Structures with the Program Package ToposPro</a>, Crystal Growth & Design, Vol. 14, No. 7 (2014), 3576-3586.
%H R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</a>
%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 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/tsc">The tsc tiling (or net)</a>
%F G.f.: (1 + x)^3 * (1 - x + x^2) * (1 + x^2) * (1 + x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + 3*x^8 + x^9 + 2*x^10 + x^11 + x^12 + x^13 + x^14 + x^16) / ((1 - x)^3 * (1 - x + x^2 - x^3 + x^4) * (1 + x + x^2 + x^3 + x^4) * (1 + x^3 + x^6) * (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - _Colin Barker_, Dec 20 2015
%F From _N. J. A. Sloane_, Feb 22 2018 (Start)
%F The following is another conjectured recurrence, found by gfun, using the command rec:=gfun[listtorec](t1, a(n)); (where t1 is a list of the initial terms) suggested by _Paul Zimmermann_.
%F Note: this should not be used to extend the sequence.
%F 0 = (-38*n^3-836*n^2-5367*n)*a(n)+(-76*n^2-798*n)*a(n+1)+(-38*n^3-912*n^2-6165*n)*a(n+2)+(-38*n^3-988*n^2-6963*n)*a(n+3)+(-38*n^3-1064*n^2-7761*n)*a(n+4)+(-38*n^3-1140*n^2-8559*n)*a(n+5)+(-76*n^3-2052*n^2-14724*n)*a(n+6)
%F + (-532*n^2-5586*n)*a(n+7)+(-76*n^3-2204*n^2-16320*n)*a(n+8)+(-684*n^2-7182*n)*a(n+9)+(-684*n^2-7182*n)*a(n+10)+(-684*n^2-7182*n)*a(n+11)+(-684*n^2-7182*n)*a(n+12)+(76*n^3+988*n^2+3552*n)*a(n+13)+(-532*n^2-5586*n)*a(n+14)
%F + (76*n^3+1140*n^2+5148*n)*a(n+15)+(38*n^3+456*n^2+1377*n)*a(n+16)+(38*n^3+532*n^2+2175*n)*a(n+17)+(38*n^3+608*n^2+2973*n)*a(n+18)
%F + (38*n^3+684*n^2+3771*n)*a(n+19)+(-76*n^2-798*n)*a(n+20)+(38*n^3+760*n^2+4569*n)*a(n+21), with
%F a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 17, a(4) = 28, a(5) = 41, a(6) = 56, a(7) = 73, a(8) = 93, a(9) = 117, a(10) = 146, a(11) = 180, a(12) = 216, a(13) = 253, a(14) = 291, a(15) = 329, a(16) = 369, a(17) = 414, a(18) = 466, a(19) = 524, a(20) = 586, a(21) = 650.
%F (End)
%Y Cf. A033616, A299903 (partial sums).
%K nonn
%O 0,2
%A _Ralf W. Grosse-Kunstleve_
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