Search: id:A107464
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%I A107464
%S A107464 11,51,175,527,1471,3903,9983,24831,144383,339967,790527,1818623,
%T A107464 4145151,9371647,21037055,46923775,104071167
%N A107464 Number of fuzzy subgroups of rank 3 cyclic group of order (p^n)*q*r where 
               p, q and r are three distinct prime.
%C A107464 It would be good to find a formula for a(n,m,l) or generating function 
               for the number of chains in the lattice of subgroups ( these are 
               the fuzzy subgroups )of the direct sum Z_(p^n) + Z_(q^m) + Z_(r^l) 
               for given 3 distinct prime p,q and r and for integers n,m and l.
%D A107464 V. Murali, Number of chains in the power set of a set with (n+2) elements, 
               specification n^1 1^2, preprint, 2005.
%D A107464 V. Murali and B. B. Makamba, Fuzzy subgroups of finite Abelian groups 
               III, Rhodes University Preprint, 2005.
%H A107464 V. Murali, <a href="http://www.ru.ac.za/affiliates/fuzzysystems">FSRG, 
               Rhodes University</a>.
%F A107464 a(n) = 2^(n+1)*(n^2 + 6n + 6) - 1
%e A107464 a(5) = (2^6)*(5^2+6*5+6)-1= 3903. This is the number of chains in the 
               lattice of subgroups of the direct sum Z_(p^6)+ Z_q + Z_r for 3 distinct 
               prime p,q and r where Z_i is the group of integers modulo i.
%Y A107464 Cf. A007047, A107392.
%Y A107464 Sequence in context: A026684 A067983 A051843 this_sequence A027942 A004622 
               A045471
%Y A107464 Adjacent sequences: A107461 A107462 A107463 this_sequence A107465 A107466 
               A107467
%K A107464 easy,nonn
%O A107464 0,1
%A A107464 Venkat Murali (v.murali(AT)ru.ac.za), May 27 2005

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