%I #32 Apr 10 2018 08:26:36
%S 1,4,9,16,25,37,53,74,99,125,151,177,205,238,279,328,381,434,483,528,
%T 574,627,690,762,840,919,995,1068,1140,1214,1294,1382,1477,1577,1681,
%U 1787,1892,1995,2096,2197,2303,2419,2546,2681,2819,2954,3082,3205,3329
%N Coordination sequence T1 for Zeolite Code TSC.
%C First 127 terms computed by _Davide M. Proserpio_ using ToposPro.
%H R. W. Grosse-Kunstleve, <a href="/A033616/b033616.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, D. M. Proserpio, <a href="http://pubs.acs.org/doi/pdf/10.1021/cg500498k">Applied Topological Analysis of Crystal Structures with the Program Package ToposPro</a>, Cryst. Growth Des. 2014, 14, 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^2) * (1 - x + 2*x^2 - x^3 + 3*x^4 - x^5 + 4*x^6 - x^7 + 4*x^8 - x^9 + 4*x^10 - x^11 + 4*x^12 - x^13 + 3*x^14 - x^15 + 2*x^16 - x^17 + x^18) / ((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 19 2015
%F From _N. J. A. Sloane_, Feb 22 2018 (Start)
%F The following is a 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^2-5351*n)*a(n)+(-76*n^2-798*n)*a(n+1)+(-38*n^3-912*n^2-6149*n)*a(n+2)+(-38*n^3-988*n^2-6947*n)*a(n+3)+(-38*n^3-1064*n^2-7745*n)*a(n+4)+(-38*n^3-1140*n^2 -8543*n)*a(n+5)+(-76*n^3-2052*n^2-14692*n)*a(n+6)
%F + (-532*n^2-5586*n)*a(n+7)+(-76*n^3-2204*n^2-16288*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+3520*n)*a(n+13)+(-532*n^2-5586*n)*a(n+14)+(76*n^3+1140*n^2+5116*n)*a(n+15)
%F + (38*n^3+456*n^2+1361*n)*a(n+16)+(38*n^3+532*n^2+2159*n)*a(n+17)+(38*n^3+608*n^2+2957*n)*a(n+18)+(38*n^3+684*n^2+3755*n)*a(n+19)+(-76*n^2-798*n)*a(n+20)+(38*n^3+760*n^2+4553*n)*a(n+21), with
%F a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16, a(4) = 25, a(5) = 37, a(6) = 53, a(7) = 74, a(8) = 99, a(9) = 125, a(10) = 151, a(11) = 177, a(12) = 205, a(13) = 238, a(14) = 279, a(15) = 328, a(16) = 381, a(17) = 434, a(18) = 483, a(19) = 528, a(20) = 574, a(21) = 627
%F (End)
%Y Cf. A033617 (second type), A299902 (partial sums).
%K nonn
%O 0,2
%A _Ralf W. Grosse-Kunstleve_