A033617 Coordination sequence T2 for Zeolite Code TSC.
1, 4, 9, 17, 28, 41, 56, 73, 93, 117, 146, 180, 216, 253, 291, 329, 369, 414, 466, 524, 586, 650, 712, 773, 836, 902, 973, 1051, 1136, 1224, 1313, 1403, 1492, 1581, 1673, 1769, 1870, 1978, 2093, 2211, 2329, 2447, 2563, 2678, 2797, 2923, 3057, 3198, 3344
Offset: 0
Keywords
Links
- R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000 (terms 0..127 from Davide M. Proserpio)
- V. A. Blatov, A. P. Shevchenko, and D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Crystal Growth & Design, Vol. 14, No. 7 (2014), 3576-3586.
- R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
- Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
- International Zeolite Association, Database of Zeolite Structures
- Reticular Chemistry Structure Resource (RCSR), The tsc tiling (or net)
Formula
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
From N. J. A. Sloane, Feb 22 2018 (Start)
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.
Note: this should not be used to extend the sequence.
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)
+ (-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)
+ (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)
+ (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
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.
(End)
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