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Search: id:A107464
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| A107464 |
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Number of fuzzy subgroups of rank 3 cyclic group of order (p^n)*q*r where p, q and r are three distinct prime. |
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+0
5
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| 11, 51, 175, 527, 1471, 3903, 9983, 24831, 144383, 339967, 790527, 1818623, 4145151, 9371647, 21037055, 46923775, 104071167
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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.
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REFERENCES
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V. Murali, Number of chains in the power set of a set with (n+2) elements, specification n^1 1^2, preprint, 2005.
V. Murali and B. B. Makamba, Fuzzy subgroups of finite Abelian groups III, Rhodes University Preprint, 2005.
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LINKS
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V. Murali, FSRG, Rhodes University.
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FORMULA
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a(n) = 2^(n+1)*(n^2 + 6n + 6) - 1
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EXAMPLE
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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.
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CROSSREFS
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Cf. A007047, A107392.
Adjacent sequences: A107461 A107462 A107463 this_sequence A107465 A107466 A107467
Sequence in context: A026684 A067983 A051843 this_sequence A027942 A004622 A045471
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KEYWORD
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easy,nonn
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AUTHOR
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Venkat Murali (v.murali(AT)ru.ac.za), May 27 2005
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