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

0,2

Comments

First 127 terms computed by Davide M. Proserpio using ToposPro.

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)

Crossrefs

Cf. A033616, A299903 (partial sums).

Sequence in context: A019572 A048205 A078567 * A033613 A033608 A008577

Adjacent sequences: A033614 A033615 A033616 * A033618 A033619 A033620

Keyword

nonn

Author

Ralf W. Grosse-Kunstleve

Status

approved