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A004068 Number of atoms in dodecahedron with n shells 26
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; text; 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

a(n+1) is the number of triples (w,x,y) having all terms in {0,...,n} and x+y>=w. [Clark Kimberling, Jun 14 2012]

a(n) = sum(A215630(n,k): k=1..n) for n > 0. - Reinhard Zumkeller, Nov 11 2012

a(n)-a(n-2)=A010001(n-1), for n>1 - K. G. Stier, Dec 21 2012

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

(Maxima) A004068(n):=5*n^3/6+n/6$ makelist(A004068(n), n, 0, 20); /* Martin Ettl, Jan 07 2013 */

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: A098334 A038796 A211791 * A022815 A172252 A027116

Adjacent sequences:  A004065 A004066 A004067 * A004069 A004070 A004071

KEYWORD

nonn,easy

AUTHOR

Albert D. Rich (Albert_Rich(AT)msn.com).

STATUS

approved

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Last modified May 20 18:12 EDT 2013. Contains 225464 sequences.