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Search: id:A004068
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| A004068 |
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Number of atoms in dodecahedron with n shells. |
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+0
22
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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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COMMENT
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Also as a(n)=(1/6)*(5*n^3+n), 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.
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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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FORMULA
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5*C(n + 1, 3) + C(n, 1). Or, with different offset, 5*n^3/6+n/6.
a(n) = sum(1 + sum(5*n)) = sum (A005891) - Xavier Acloque Oct 08 2003
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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.
Adjacent sequences: A004065 A004066 A004067 this_sequence A004069 A004070 A004071
Sequence in context: A147121 A098334 A038796 this_sequence A022815 A027116 A151718
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KEYWORD
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nonn
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AUTHOR
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Albert D. Rich (Albert_Rich(AT)msn.com).
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