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A004068
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Number of atoms in dodecahedron with n shells
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26
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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
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (3).
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LINKS
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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)
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FORMULA
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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
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MATHEMATICA
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Table[5*n^3/6+n/6, {n, 0, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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PROG
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(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 */
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Albert D. Rich (Albert_Rich(AT)msn.com).
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STATUS
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approved
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