A008000 -id:A008000 - cp's OEIS frontend

A008137 Coordination sequence T1 for Zeolite Code LTA and RHO.

1, 4, 9, 17, 28, 42, 60, 81, 105, 132, 162, 196, 233, 273, 316, 362, 412, 465, 521, 580, 642, 708, 777, 849, 924, 1002, 1084, 1169, 1257, 1348, 1442, 1540, 1641, 1745, 1852, 1962, 2076, 2193, 2313, 2436, 2562, 2692, 2825, 2961, 3100, 3242, 3388, 3537, 3689

Offset: 0

Ralf W. Grosse-Kunstleve

Also, growth series for the affine Coxeter (or Weyl) groups B_3. - N. J. A. Sloane, Jan 11 2016

Also, coordination sequence for "rho" 3D uniform tiling. - N. J. A. Sloane, Feb 10 2018

N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tilings #25 and 27.
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
Reticular Chemistry Structure Resource (RCSR), The lta tiling (or net)
Reticular Chemistry Structure Resource (RCSR), The rho tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175.
For partial sums see A299276.
The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e:  A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

(1-x^2)*(1-x^4)*(1-x^6)/((1-x)^4*(1-x^3)*(1-x^5));
seq(coeff(series(%,x,n+1),x,n), n=0..48);

a(5*m+k) = 40*m^2 + 16*k*m + one of 5 numbers depending on k, 0 <= k < 5 (N. J. A. Sloane).
G.f.: (1-x^2)*(1-x^4)*(1-x^6)/((1-x)^4*(1-x^3)*(1-x^5)). This can also be written as (x+1)^3*(x^2+1)*(x^2-x+1)/((1-x)^3*(x^4+x^3+x^2+x+1)). - N. J. A. Sloane, Feb 10 2018
a(n) = 12/5 - 0^n + (8/5)*n^2 - (1/25)*(5+sqrt(5))*cos(2*Pi*n/5) - (1/25)*(5-sqrt(5))*cos(4*Pi*n/5). - Eric Simon Jacob, Feb 12 2023

A008253 Coordination sequence for diamond.

Original entry on oeis.org

1, 4, 12, 24, 42, 64, 92, 124, 162, 204, 252, 304, 362, 424, 492, 564, 642, 724, 812, 904, 1002, 1104, 1212, 1324, 1442, 1564, 1692, 1824, 1962, 2104, 2252, 2404, 2562, 2724, 2892, 3064, 3242, 3424, 3612, 3804, 4002, 4204, 4412, 4624, 4842, 5064, 5292, 5524

Offset: 0

N. J. A. Sloane, Ralf W. Grosse-Kunstleve

Inorganic Crystal Structure Database: Collection Code 9327.

N. J. A. Sloane, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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
M. O'Keeffe, M. A. Peskov, S. J. Ramsden, and O. M. Yaghi, The reticular chemistry structure resource (RCSR) database of, and symbols for, crystal nets, Accounts of Chemical Research, (2008), 1782-1789. See p. 1786.
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Cf. A007904, A047209.

{1}~Join~Table[2 (2 + Sum[Floor[(5 k + 3)/2], {k, n - 1}]), {n, 50}] (* Alexander Adamchuk, May 23 2006, edited by Michael De Vlieger, May 31 2022 *)

Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, Mar 21 2017

G.f.: (1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)).
a(2*m) = 10*m^2+2, a(2*m+1) = 10*m^2+10*m+4 (N. J. A. Sloane).
Apart from first term, first differences of A007904(n). - Alexander Adamchuk, May 23 2006
a(n) = 2* ( 2 + Sum_{k=1..n-1} floor((5*k+3)/2) ). - Alexander Adamchuk, May 23 2006
From Colin Barker, Mar 21 2017: (Start)
a(n) = (5*n^2 + 4)/2 for n>0 and even.
a(n) = (5*n^2 + 3)/2 for n odd.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
(End)

A008084 Coordination sequence T1 for Zeolite Code ACO, ASV, EDI, and THO.

Original entry on oeis.org

1, 4, 9, 19, 35, 52, 72, 100, 131, 163, 201, 244, 290, 340, 393, 451, 515, 580, 648, 724, 803, 883, 969, 1060, 1154, 1252, 1353, 1459, 1571, 1684, 1800, 1924, 2051, 2179, 2313, 2452, 2594, 2740, 2889, 3043, 3203, 3364, 3528, 3700, 3875, 4051, 4233, 4420

Offset: 0

Ralf W. Grosse-Kunstleve

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

Vincenzo Librandi, 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.
Reticular Chemistry Structure Resource, nets pcb, pcb-b, asv, edi, edi-c.
Index entries for linear recurrences with constant coefficients, signature (2,-2,3,-3,2,-2,1).

CoefficientList[Series[-(x + 1)^3 (x^4 - x^3 + 3 x^2 - x + 1)/((x - 1)^3 (x^2 + 1) (x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)

For n > 1, a(n) = 2n^2 - 4n + 4 + p(n), with the 12-periodic sequence p(n) with period {0, 0, 0, -1, -1, 1, 0, -2, 0, 1, -1, -1}.
a(12*m+k) = 288*m^2 + 48*k*m + [ 2, 4, 9, 19, 35, 52, 72, 100, 131, 163, 201, 244 ], 0 <= k < 12. - N. J. A. Sloane
G.f.: -(x+1)^3*(x^4-x^3+3*x^2-x+1) / ((x-1)^3*(x^2+1)*(x^2+x+1)). - Colin Barker, Dec 12 2012

A008264 Coordination sequence for tridymite, lonsdaleite, and wurtzite.

Original entry on oeis.org

1, 4, 12, 25, 44, 67, 96, 130, 170, 214, 264, 319, 380, 445, 516, 592, 674, 760, 852, 949, 1052, 1159, 1272, 1390, 1514, 1642, 1776, 1915, 2060, 2209, 2364, 2524, 2690, 2860, 3036, 3217, 3404, 3595, 3792, 3994, 4202, 4414, 4632, 4855, 5084, 5317, 5556, 5800

Offset: 0

Ralf W. Grosse-Kunstleve

Inorganic Crystal Structure Database: Collection Code 29343
Michael O'Keeffe, Topological and geometrical characterization of sites in silicon carbide polytypes, Chemistry of Materials 3 (2) (1991), 332-335. (Eq. (2) gives an empirical formula for a(n). - N. J. A. Sloane, Apr 07 2018)

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
M. L. Glasser, Symmetry properties of the wurtzite structure, Journal of Physics and Chemistry of Solids, 10(2-3) (1959), 229-241.
Ralf W. Grosse-Kunstleve, Zeolites, Frameworks, Coordination Sequences and Encyclopedia of Integer Sequences, 1996.
Ralf 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), 879-889.
Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane.
Michael O'Keeffe, N-dimensional diamond, sodalite and rare sphere packings, Acta Cryst. A 47 (1991), 749-753.
Michael O'Keeffe, Topological and geometrical characterization of sites in silicon carbide polytypes, Chemistry of Materials 3 (2) (1991), 332-335.
Reticular Chemistry Structure Resource (RCSR), The lon net (lonsdaleite) and The lon-b net (wurtzite).
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Cf. A008524 for 4-D analog, A008253 for diamond.

Cf. A217511 for theta series.

a[n_] := (m = Quotient[n, 4]; k = Mod[n, 4]; 42*m^2 + 21*k*m + Switch[k, 0, 2, 1, 4, 2, 12, 3, 25]); a[0]=1; Table[a[n], {n, 0, 47}] (* Jean-François Alcover, Oct 11 2012, from the first formula *)
Join[{1}, Table[1 + (42 n^2 + (1 + (-1)^n) (3 + 2 (-1)^((n - 1) n/2)) + 6)/16, {n, 50}]] (* Bruno Berselli, Jul 24 2013 *)
LinearRecurrence[{2,-1,0,1,-2,1},{1,4,12,25,44,67,96},20] (* Harvey P. Dale, Dec 27 2016 *)

a(n)=if(n, 1+(42*n^2+(1+(-1)^n)*(3+2*(-1)^((n-1)*n/2))+6)/16, 1) \\ Charles R Greathouse IV, Feb 10 2017

a(4*m+k) = 42*m^2 + 21*k*m + [ 2, 4, 12, 25 ], 0 <= k < 4 (N. J. A. Sloane).
a(n) = 1 + (42*n^2 + (1 + (-1)^n)*(3 + 2*(-1)^((n - 1)*n/2)) + 6)/16 for n > 0, a(0) = 1. - Bruno Berselli, Jul 24 2013
G.f.: (1 + 2*x + 5*x^2 + 5*x^3 + 5*x^4 + 2*x^5 + x^6)/((1 - x)^3*(1 + x + x^2 + x^3)). - Bruno Berselli, Jul 24 2013

A019456 Coordination sequence T1 for Zeolite Code CZP.

Original entry on oeis.org

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

cp's OEIS Frontend

A008137 Coordination sequence T1 for Zeolite Code LTA and RHO.

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Maple

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A008253 Coordination sequence for diamond.

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PARI

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A008084 Coordination sequence T1 for Zeolite Code ACO, ASV, EDI, and THO.

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Mathematica

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A008264 Coordination sequence for tridymite, lonsdaleite, and wurtzite.

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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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