Search: id:A004068
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%I A004068
%S A004068 0,1,7,23,54,105,181,287,428,609,835,1111,1442,1833,2289,2815,3416,
%T A004068 4097,4863,5719,6670,7721,8877,10143,11524,13025,14651,16407,18298,
%U A004068 20329,22505,24831,27312,29953,32759,35735,38886,42217,45733,49439
%N A004068 Number of atoms in dodecahedron with n shells.
%C A004068 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.
%D A004068 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (3).
%F A004068 5*C(n + 1, 3) + C(n, 1). Or, with different offset, 5*n^3/6+n/6.
%F A004068 a(n) = sum(1 + sum(5*n)) = sum (A005891) - Xavier Acloque Oct 08 2003
%Y A004068 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.
%Y A004068 Cf. A005891, A006322.
%Y A004068 Sequence in context: A147121 A098334 A038796 this_sequence A022815 A027116 
               A151718
%Y A004068 Adjacent sequences: A004065 A004066 A004067 this_sequence A004069 A004070 
               A004071
%K A004068 nonn
%O A004068 0,3
%A A004068 Albert D. Rich (Albert_Rich(AT)msn.com).

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