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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).

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Last modified February 12 11:44 EST 2012. Contains 205378 sequences.