cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A119876 Number of faces of the root-n Waterman polyhedron of void-center type as defined in A119870.

Original entry on oeis.org

8, 6, 14, 14, 56, 26, 14, 14, 50, 62, 26, 26, 32, 102, 50, 50, 38, 26, 74, 74, 134, 134, 50, 50, 68, 62, 74, 74, 122, 50, 134, 134, 50, 146, 74, 74, 110, 114, 146, 146, 140, 74, 134, 134, 170, 122, 74, 74, 98, 158, 194, 194, 146, 122, 74, 74, 134, 86, 122, 122, 164
Offset: 0

Views

Author

Hugo Pfoertner, Jun 05 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119874, A119871 [faces of Waterman polyhedron of basic type].

A119877 Number of edges of the root-n Waterman polyhedron of void-center type as defined in A119870.

Original entry on oeis.org

12, 12, 36, 36, 84, 48, 36, 36, 96, 108, 72, 72, 60, 156, 120, 120, 84, 72, 144, 144, 228, 228, 120, 120, 120, 156, 144, 144, 216, 120, 252, 252, 144, 264, 168, 168, 204, 192, 288, 288, 240, 192, 276, 276, 312, 288, 168, 168, 192, 252, 360, 360, 336, 288, 192
Offset: 0

Views

Author

Hugo Pfoertner, Jun 05 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119874, A119872 [edges of Waterman polyhedron of basic type].

A119878 3*Volume of the root-n Waterman polyhedron of void-center type as defined in A119870.

Original entry on oeis.org

4, 24, 96, 96, 272, 344, 404, 404, 712, 844, 988, 988, 1156, 1500, 1740, 1740, 1992, 2088, 2316, 2316, 3032, 3128, 3344, 3344, 3692, 3968, 4206, 4206, 4768, 5032, 5428, 5428, 5896, 6184, 6448, 6448, 6772, 7284, 7812, 7812, 8496, 8664, 8988, 8988, 9780
Offset: 0

Views

Author

Hugo Pfoertner, Jun 05 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119874, A119873 [volume of Waterman polyhedron of basic type].

A119871 Number of faces of the root-n Waterman polyhedron as defined in A119870.

Original entry on oeis.org

14, 8, 26, 14, 14, 42, 26, 68, 38, 14, 50, 26, 74, 74, 26, 38, 62, 44, 74, 50, 74, 50, 26, 66, 134, 62, 122, 74, 50, 50, 50, 92, 122, 98, 74, 134, 134, 122, 74, 50, 146, 74, 170, 170, 98, 98, 122, 122, 134, 176, 146, 74, 146, 258, 122, 122, 146, 146, 194, 146
Offset: 1

Views

Author

Hugo Pfoertner, May 26 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119870, A119876 [faces of void-centered Waterman polyhedron].

A119872 Number of edges of the root-n Waterman polyhedron as defined in A119870.

Original entry on oeis.org

24, 12, 48, 24, 36, 72, 72, 120, 72, 36, 96, 48, 144, 144, 72, 96, 108, 96, 144, 120, 144, 120, 72, 120, 264, 156, 240, 168, 120, 120, 144, 192, 216, 192, 192, 216, 252, 264, 168, 120, 264, 144, 336, 336, 216, 216, 264, 288, 240, 300, 312, 144, 288, 408, 264, 264
Offset: 1

Views

Author

Hugo Pfoertner, May 26 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119877 [edges of void-centered Waterman polyhedron].

A119873 3*Volume of the root-n Waterman polyhedron as defined in A119870.

Original entry on oeis.org

20, 32, 136, 160, 244, 348, 516, 600, 744, 768, 1016, 1088, 1484, 1484, 1628, 1700, 2092, 2272, 2608, 2680, 2920, 3040, 3136, 3432, 3996, 4092, 4620, 4716, 4788, 4788, 5220, 5424, 6224, 6368, 6512, 6920, 7400, 7520, 7616, 7688, 8228, 8322, 9412, 9508
Offset: 1

Views

Author

Hugo Pfoertner, May 26 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119878 [volume of void-centered Waterman polyhedron].

A119875 Number of vertices of the root-n Waterman polyhedron of void-center type as defined in A119870.

Original entry on oeis.org

6, 8, 24, 24, 30, 24, 24, 24, 48, 48, 48, 48, 30, 56, 72, 72, 48, 48, 72, 72, 96, 96, 72, 72, 54, 96, 72, 72, 96, 72, 120, 120, 96, 120, 96, 96, 96, 80, 144, 144, 102, 120, 144, 144, 144, 168, 96, 96, 96, 96, 168, 168, 192, 168, 120, 120, 144, 120, 168, 168, 126
Offset: 0

Views

Author

Hugo Pfoertner, Jun 05 2006

Keywords

Comments

For more information see A119870.

Crossrefs

Cf. A119869, A119874, A119870 [vertices of Waterman polyhedron of basic type].

A119869 Sizes of successive clusters in f.c.c. lattice centered at a lattice point.

Original entry on oeis.org

1, 13, 19, 43, 55, 79, 87, 135, 141, 177, 201, 225, 249, 321, 321, 369, 381, 429, 459, 531, 555, 603, 627, 675, 683, 767, 791, 887, 935, 959, 959, 1055, 1061, 1157, 1205, 1253, 1289, 1409, 1433, 1481, 1505, 1553, 1601, 1721, 1745, 1865, 1865, 1961, 1985, 2093, 2123
Offset: 0

Views

Author

Hugo Pfoertner, May 26 2006

Keywords

References

  • N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.

Links

Crossrefs

Cf. A004015, A004215, A055039.
Cf. A055039 [missing polyhedra]. Properties of Waterman polyhedra: A119870 [vertices], A119871 [faces], A119872 [edges], A119873 [volume]. Waterman polyhedra with different centers: A119874, A119875, A119876, A119877, A119878.

Programs

  • Maple
    maxd:=20001: read format: temp0:=trunc(evalf(sqrt(maxd)))+2: a:=0: for i from -temp0 to temp0 do a:=a+q^( (i+1/2)^2): od: th2:=series(a,q,maxd): a:=0: for i from -temp0 to temp0 do a:=a+q^(i^2): od: th3:=series(a,q,maxd): th4:=series(subs(q=-q,th3),q,maxd):
t1:=series((th3^3+th4^3)/2,q,maxd): t1:=series(subs(q=sqrt(q),t1),q,floor(maxd/2)): t2:=seriestolist(t1): t4:=0; for n from 1 to nops(t2) do t4:=t4+t2[n]; lprint(n-1, t4); od: # N. J. A. Sloane, Aug 09 2006
  • Mathematica
    a[n_] := Sum[SquaresR[3, 2k], {k, 0, n}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 12 2012, after formula *)
Accumulate[SquaresR[3,2*Range[0,70]]] (* Harvey P. Dale, Jun 01 2015 *)

Formula

Partial sums of A004015, which has an explicit generating function.

Extensions

Edited by N. J. A. Sloane, Aug 09 2006
Additional links from Steve Waterman, Nov 26 2006
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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