A005897 -id:A005897 - cp's OEIS frontend

A009858 Coordination sequence T4 for Zeolite Code -PAR.

1, 3, 8, 16, 29, 49, 68, 94, 123, 162, 203, 229, 276, 334, 400, 446, 481, 569, 654, 723, 781, 847, 971, 1064, 1129, 1229, 1331, 1463, 1550, 1645, 1799, 1901, 2041, 2141, 2275, 2469, 2559, 2716, 2847, 3003, 3221, 3324, 3499, 3645, 3828, 4083, 4188, 4380

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

A009943 Coordination sequence for NiAs(1), As position.

Original entry on oeis.org

1, 6, 24, 56, 96, 152, 216, 296, 384, 488, 600, 728, 864, 1016, 1176, 1352, 1536, 1736, 1944, 2168, 2400, 2648, 2904, 3176, 3456, 3752, 4056, 4376, 4704, 5048, 5400, 5768, 6144, 6536, 6936, 7352, 7776, 8216, 8664, 9128, 9600, 10088, 10584

Offset: 0

Ralf W. Grosse-Kunstleve

nonn

Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (194) hP4.

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

(1+4*x+12*x^2+10*x^3-5*x^4+2*x^5)/(1-x^2)/(1-x)^2;

A085690 Number of intersections between a sphere inscribed in a cube and the n X n X n cubes resulting from a cubic lattice subdivision of the enclosing cube.

Original entry on oeis.org

8, 26, 56, 98, 152, 194, 272, 362, 440, 530, 656, 746, 872, 1034, 1160, 1298, 1496, 1658, 1856, 1994, 2240, 2450, 2624, 2906, 3128, 3362, 3656, 3890, 4208, 4442, 4760, 5090, 5360, 5714, 6032, 6362, 6752, 7106, 7496, 7826, 8216, 8618, 9080, 9458, 9896

Offset: 2

Hugo Pfoertner, Jul 17 2003

nonn

A concise description of the problem is given by Clive Tooth in the Seaman, Tooth link. Sequence terms up to n=10 were first given by Dave Seaman. Cubes having at least one vertex on the sphere and all other vertices either all inside or all outside the sphere are counted as 1/2. a(n) is asymptotic to (3/2)*Pi*n^2. (Clive Tooth) The terms a(2),...,a(6) are identical with A005897(n-1) (points on surface of cube with square grid on its faces).

			a(2)=8 because all 8 cubes resulting from a 2*2*2 subdivision of a cube are intersected by a sphere inscribed in the large cube.
a(4)=56: 8 central cubes of 4*4*4=64 not intersected.

Hugo Pfoertner, Table of n, a(n) for n = 2..1000
Hugo Pfoertner, FORTRAN program to count intersections.
Dave Seaman, Clive Tooth, Sphere/Cube Intersections. Discussion in Newsgroup sci.math.

Cf. A005897, A008574.

Fortran
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Corrected overflow in program and b-file by Hugo Pfoertner, Apr 09 2016

A262067 a(n) = n^n - (n-2)^n.

Original entry on oeis.org

2, 4, 26, 240, 2882, 42560, 745418, 15097600, 347066882, 8926258176, 253930611002, 7916100448256, 268352394448322, 9828088361009152, 386707997366768618, 16268790735900180480, 728714136550643404802, 34624041592426892361728

Offset: 1

Altug Alkan, Sep 10 2015

Inspired by multi-dimensional cubes: For n>1, the number of lattice points on the surface of a k-dimensional cube with side-length n is f(n,k) = n^k - (n-2)^k. a(n) = f(n,n).

			For n = 2, a(n) = n^n - (n-2)^n = 2^2 - (2-2)^2 = 4.

Cf. A000312, A008788.

For sequences with "Number of points on surface of k-dimensional cube," cf. A130130 (k=1), A008574 (k=2, shifted), A005897 (k=3), A008511 (k=4), A008512 (k=5), A008513 (k=6).

[n^n - (n-2)^n : n in [1..20]]; // Wesley Ivan Hurt, Sep 10 2015

A262067:=n->n^n - (n-2)^n: seq(A262067(n), n=1..20); # Wesley Ivan Hurt, Sep 10 2015

Array[#^# - (# - 2)^# &, {18}] (* Michael De Vlieger, Sep 10 2015 *)

a(n) = n^n - (n-2)^n;
vector(40, n, a(n))

a(n) = A000312(n) - A008788(n-2).

A008001 Coordination sequence T1 for Zeolite Code AEI.

Original entry on oeis.org

1, 4, 9, 17, 29, 45, 64, 85, 111, 143, 177, 213, 253, 297, 345, 396, 449, 506, 568, 633, 702, 774, 847, 925, 1008, 1094, 1184, 1276, 1371, 1472, 1577, 1684, 1793, 1906, 2024, 2145, 2269, 2396, 2526, 2660, 2798, 2941, 3088, 3236, 3387, 3544, 3704, 3866, 4032

Offset: 0

Ralf W. Grosse-Kunstleve

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

(1-x)*(1+7*x^2+13*x^3+22*x^4+33*x^5+45*x^6+57*x^7+71*x^8+85*x^9+
99*x^10+111*x^11+123*x^12+132*x^13+139*x^14+142*x^15+143*x^16+
142*x^17+139*x^18+132*x^19+123*x^20+111*x^21+99*x^22+85*x^23+
71*x^24+3*x+57*x^25+45*x^26+33*x^27+22*x^28+7*x^30+3*x^31+x^32+
13*x^29)*(x+1)^2/(1-x^3)/(1-x^5)/(1-x^11)/(1-x^16);

A008002 Coordination sequence T2 for Zeolite Code AEI.

Original entry on oeis.org

1, 4, 9, 17, 29, 45, 65, 88, 113, 143, 178, 214, 253, 297, 345, 395, 448, 508, 570, 632, 700, 774, 851, 927, 1007, 1096, 1185, 1275, 1372, 1474, 1577, 1681, 1793, 1910, 2025, 2142, 2267, 2398, 2528, 2660, 2800, 2944, 3088, 3235, 3389, 3546, 3703, 3864, 4031

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

A008003 Coordination sequence T3 for Zeolite Code AEI.

Original entry on oeis.org

1, 4, 9, 17, 29, 45, 65, 87, 113, 143, 176, 214, 253, 297, 345, 395, 451, 507, 568, 634, 700, 772, 848, 928, 1010, 1093, 1184, 1278, 1373, 1472, 1575, 1684, 1793, 1905, 2025, 2146, 2268, 2394, 2528, 2665, 2800, 2940, 3086, 3237, 3388, 3542, 3704, 3867, 4032

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

A008004 Coordination sequence T1 for Zeolite Code AEL.

Original entry on oeis.org

1, 4, 11, 21, 37, 59, 85, 114, 150, 189, 232, 279, 331, 390, 455, 519, 589, 667, 748, 831, 921, 1015, 1115, 1220, 1327, 1439, 1560, 1679, 1802, 1936, 2073, 2213, 2361, 2507, 2659, 2820, 2982, 3150, 3327, 3501, 3681, 3871, 4061, 4254, 4458, 4661, 4868, 5085

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

A008005 Coordination sequence T2 for Zeolite Code AEL.

Original entry on oeis.org

1, 4, 11, 22, 38, 58, 85, 115, 148, 188, 234, 280, 333, 390, 450, 519, 593, 666, 748, 833, 919, 1016, 1118, 1217, 1327, 1441, 1554, 1679, 1810, 1936, 2073, 2213, 2352, 2507, 2667, 2819, 2984, 3153, 3319, 3501, 3688, 3867, 4061, 4258, 4450, 4661, 4878, 5083

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 + 4*x + 11*x^2 + 22*x^3 + 37*x^4 + 54*x^5 + 73*x^6 + 89*x^7 + 99*x^8 + 108*x^9 + 112*x^10 + 111*x^11 + 111*x^12 + 109*x^13 + 106*x^14 + 109*x^15 + 111*x^16 + 111*x^17 + 112*x^18 + 108*x^19 + 99*x^20 + 89*x^21 + 73*x^22 + 54*x^23 + 37*x^24 + 22*x^25 + 11*x^26 + 4*x^27 + x^28) / (1-x^4) / (1-x^6) / (1-x^18). - Sean A. Irvine, Mar 13 2018

A008006 Coordination sequence T3 for Zeolite Code AEL.

Original entry on oeis.org

1, 4, 12, 24, 40, 59, 84, 115, 150, 186, 230, 282, 336, 390, 452, 520, 592, 667, 746, 833, 928, 1018, 1112, 1218, 1328, 1440, 1558, 1678, 1806, 1939, 2072, 2211, 2360, 2508, 2660, 2822, 2986, 3152, 3328, 3502, 3680, 3869, 4060, 4257, 4462, 4660, 4866, 5086

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

A009858 Coordination sequence T4 for Zeolite Code -PAR.

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A009943 Coordination sequence for NiAs(1), As position.

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A085690 Number of intersections between a sphere inscribed in a cube and the n X n X n cubes resulting from a cubic lattice subdivision of the enclosing cube.

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A262067 a(n) = n^n - (n-2)^n.

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Magma

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PARI

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A008001 Coordination sequence T1 for Zeolite Code AEI.

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Maple

A008002 Coordination sequence T2 for Zeolite Code AEI.

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A008003 Coordination sequence T3 for Zeolite Code AEI.

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A008004 Coordination sequence T1 for Zeolite Code AEL.

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A008005 Coordination sequence T2 for Zeolite Code AEL.

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A008006 Coordination sequence T3 for Zeolite Code AEL.

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