A005897 -id:A005897 - cp's OEIS frontend

A019456 Coordination sequence T1 for Zeolite Code CZP.

1, 4, 9, 18, 32, 54, 83, 113, 149, 191, 234, 281, 342, 399, 459, 537, 611, 678, 763, 861, 947, 1035, 1151, 1267, 1367, 1481, 1611, 1738, 1862, 1995, 2140, 2291, 2443, 2591, 2751, 2929, 3094, 3252, 3439, 3639, 3816, 3995, 4211, 4427, 4618, 4823, 5055

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

Cf. A019457, A019458.

A019457 Coordination sequence T2 for Zeolite Code CZP.

Original entry on oeis.org

1, 4, 10, 20, 33, 56, 85, 114, 144, 192, 242, 280, 333, 412, 475, 526, 602, 698, 776, 850, 949, 1058, 1157, 1258, 1372, 1500, 1620, 1732, 1863, 2020, 2161, 2280, 2434, 2624, 2778, 2910, 3087, 3294, 3463, 3618, 3818, 4038, 4228, 4410, 4625, 4864, 5075

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

Cf. A019456, A019458.

A019458 Coordination sequence T3 for Zeolite Code CZP.

Original entry on oeis.org

1, 4, 8, 16, 33, 52, 73, 112, 160, 190, 214, 282, 351, 386, 439, 548, 624, 658, 742, 872, 953, 1012, 1127, 1276, 1380, 1462, 1582, 1744, 1877, 1970, 2101, 2302, 2464, 2558, 2710, 2948, 3113, 3210, 3397, 3660, 3834, 3952, 4166, 4444, 4637, 4782, 5005

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

Cf. A019456, A019457.

A033616 Coordination sequence T1 for Zeolite Code TSC.

Original entry on oeis.org

1, 4, 9, 16, 25, 37, 53, 74, 99, 125, 151, 177, 205, 238, 279, 328, 381, 434, 483, 528, 574, 627, 690, 762, 840, 919, 995, 1068, 1140, 1214, 1294, 1382, 1477, 1577, 1681, 1787, 1892, 1995, 2096, 2197, 2303, 2419, 2546, 2681, 2819, 2954, 3082, 3205, 3329

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, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 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. A033617 (second type), A299902 (partial sums).

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
From N. J. A. Sloane, Feb 22 2018 (Start)
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.
Note: this should not be used to extend the sequence.
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)
+ (-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)
+ (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
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
(End)

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)

A008016 Coordination sequence T2 for Zeolite Code AFO.

Original entry on oeis.org

1, 4, 11, 22, 41, 65, 88, 111, 145, 186, 231, 281, 336, 395, 455, 518, 597, 679, 752, 827, 921, 1024, 1123, 1222, 1330, 1442, 1555, 1678, 1821, 1965, 2088, 2207, 2357, 2518, 2671, 2829, 2996, 3167, 3335, 3506, 3705, 3903, 4072, 4247, 4461, 4688, 4899, 5104

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

A008040 Coordination sequence T3 for Zeolite Code ATS.

Original entry on oeis.org

1, 4, 10, 19, 32, 51, 72, 96, 124, 155, 196, 238, 278, 324, 374, 436, 500, 558, 620, 688, 772, 857, 934, 1014, 1098, 1203, 1310, 1405, 1504, 1606, 1730, 1858, 1972, 2089, 2210, 2355, 2502, 2634, 2770, 2909, 3076, 3244, 3392, 3546, 3704, 3892, 4082, 4248

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

G.f.: (1 + x) * (1 + 2*x + 5*x^2 + 7*x^3 + 13*x^4 + 16*x^5 + 18*x^6 + 20*x^7 + 18*x^8 + 16*x^9 + 13*x^10 + 7*x^11 + 5*x^12 + 2*x^13 + x^14) / ((1 - x)^3 * (1 - x + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)^2). - Colin Barker, Dec 21 2015

A008185 Coordination sequence T4 for Zeolite Code MOR.

Original entry on oeis.org

1, 4, 11, 24, 39, 60, 92, 122, 148, 195, 250, 293, 342, 403, 472, 551, 621, 690, 786, 879, 954, 1047, 1168, 1293, 1397, 1484, 1622, 1773, 1880, 2007, 2181, 2336, 2456, 2606, 2783, 2966, 3122, 3278, 3468, 3672, 3855, 4037, 4253, 4466, 4664, 4853, 5081, 5338

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

A008242 Coordination sequence T2 for Zeolite Code TON.

Original entry on oeis.org

1, 4, 12, 23, 43, 66, 91, 128, 169, 214, 258, 306, 381, 450, 509, 574, 659, 771, 848, 924, 1038, 1148, 1274, 1373, 1491, 1636, 1743, 1902, 2051, 2188, 2340, 2466, 2689, 2864, 2991, 3170, 3343, 3611, 3776, 3910, 4166, 4362, 4626, 4813, 5007, 5296, 5461, 5768

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996

R. W. Grosse-Kunstleve, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
International Zeolite Association, Database of Zeolite Structures

A008259 Coordination sequence T2 for Moganite, also for BGB1.

Original entry on oeis.org

1, 4, 11, 24, 41, 62, 90, 122, 157, 200, 247, 296, 354, 416, 479, 552, 629, 706, 794, 886, 977, 1080, 1187, 1292, 1410, 1532, 1651, 1784, 1921, 2054, 2202, 2354, 2501, 2664, 2831, 2992, 3170, 3352, 3527, 3720, 3917, 4106, 4314, 4526, 4729, 4952, 5179, 5396

Offset: 0

Ralf W. Grosse-Kunstleve, David M. Teter (dmteter(AT)sandia.gov)

Inorganic Crystal Structure Database: Collection Code 67669 (for Moganite)

Sean A. Irvine, Table of n, a(n) for n = 0..1000
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane
D. M. Teter, G.V. Gibbs, M. B. Boisen, D.C. Allan, and M. P. Teter, First principles study of several hypothetical silica framework structures, Physical Review B, 52 (1995), pp. 8064-8073.
Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

CoefficientList[Series[-(x + 1) (x^6 + 2 x^5 + 5 x^4 + 6 x^3 + 5 x^2 + 2 x + 1)/((x - 1)^3 (x^2 + x + 1)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{1,0,2,-2,0,-1,1},{1,4,11,24,41,62,90,122},70] (* Harvey P. Dale, May 10 2024 *)

a(3m) = 22m^2+2, a(3m+1) = 22m^2+15m+4, a(3m+2)=22m^2+29m+11. - N. J. A. Sloane

G.f.: -(x+1)*(x^6+2*x^5+5*x^4+6*x^3+5*x^2+2*x+1) / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Dec 12 2012

cp's OEIS Frontend

A019456 Coordination sequence T1 for Zeolite Code CZP.

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A019457 Coordination sequence T2 for Zeolite Code CZP.

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A019458 Coordination sequence T3 for Zeolite Code CZP.

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A033616 Coordination sequence T1 for Zeolite Code TSC.

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A033617 Coordination sequence T2 for Zeolite Code TSC.

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A008016 Coordination sequence T2 for Zeolite Code AFO.

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A008040 Coordination sequence T3 for Zeolite Code ATS.

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A008185 Coordination sequence T4 for Zeolite Code MOR.

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A008242 Coordination sequence T2 for Zeolite Code TON.

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A008259 Coordination sequence T2 for Moganite, also for BGB1.

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