|
| |
|
|
A004068
|
|
Number of atoms in dodecahedron with n shells
|
|
23
| |
|
|
0, 1, 7, 23, 54, 105, 181, 287, 428, 609, 835, 1111, 1442, 1833, 2289, 2815, 3416, 4097, 4863, 5719, 6670, 7721, 8877, 10143, 11524, 13025, 14651, 16407, 18298, 20329, 22505, 24831, 27312, 29953, 32759, 35735, 38886, 42217, 45733, 49439
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Also as a(n)=(n/6)*(5*n^2+1), n>0: structured pentagonal diamond numbers (vertex structure 6) (Cf. A081436 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.
Number of atoms in decahedron with n shells, number = 5/6*(n^3) + 1/6*(n) (T.P. Martin, Shells of atoms, eq.(3)). - Brigitte Stepanov, Jul 02 2011
|
|
|
REFERENCES
| T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (3).
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1)
|
|
|
FORMULA
| a(n) = 5*binomial(n + 1, 3) + binomial(n, 1).
a(n) = 5*n^3/6 + n/6.
a(n) = sum_{i=0..n-1} A005891(i). - Xavier Acloque Oct 08 2003
G.f. x*(1+3*x+x^2) / (1-x)^4 . - R. J. Mathar, Jun 05 2011
|
|
|
MATHEMATICA
| Table[5*n^3/6+n/6, {n, 0, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
|
|
|
PROG
| (MAGMA) [5*n^3/6+n/6: n in [0..50]]; // Vincenzo Librandi, May 15 2011
|
|
|
CROSSREFS
| 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.
Cf. A005891, A006322.
Sequence in context: A147121 A098334 A038796 * A022815 A172252 A027116
Adjacent sequences: A004065 A004066 A004067 * A004069 A004070 A004071
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Albert D. Rich (Albert_Rich(AT)msn.com).
|
| |
|
|
