A033616 -id:A033616 - cp's OEIS frontend

A299902 Partial sums of A033616.

1, 5, 14, 30, 55, 92, 145, 219, 318, 443, 594, 771, 976, 1214, 1493, 1821, 2202, 2636, 3119, 3647, 4221, 4848, 5538, 6300, 7140, 8059, 9054, 10122, 11262, 12476, 13770, 15152, 16629, 18206, 19887, 21674, 23566, 25561, 27657, 29854, 32157, 34576, 37122, 39803, 42622, 45576, 48658, 51863, 55192, 58652, 62255, 66013, 69933, 74015, 78255, 82649, 87195, 91896, 96758, 101788, 106993

Offset: 0

N. J. A. Sloane, Feb 21 2018

nonn

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

Cf. A033616.

A033617 Coordination sequence T2 for Zeolite Code TSC.

Original entry on oeis.org

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

Ralf W. Grosse-Kunstleve

nonn

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

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)

Cf. A033616, A299903 (partial sums).

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)

cp's OEIS Frontend

A299902 Partial sums of A033616.

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