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URL: https://oeis.org/A107464

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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.
5
11, 51, 175, 527, 1471, 3903, 9983, 24831, 60415, 144383, 339967, 790527, 1818623, 4145151, 9371647, 21037055, 46923775, 104071167, 229638143, 504365055, 1103101951, 2403336191, 5217714175, 11291066367, 24360517631, 52412022783, 112474456063, 240786604031
OFFSET
0,1
COMMENTS
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.
REFERENCES
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.
FORMULA
a(n) = 2^(n+1)*(n^2 + 6n + 6) - 1.
G.f.: (16*x^2-26*x+11) / ((x-1)*(2*x-1)^3). - Colin Barker, Jan 15 2015
EXAMPLE
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.
PROG
(PARI) Vec((16*x^2-26*x+11)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Jan 15 2015
CROSSREFS
Sequence in context: A226451 A185505 A051843 * A027942 A168214 A321421
KEYWORD
easy,nonn
AUTHOR
Venkat Murali (v.murali(AT)ru.ac.za), May 27 2005
EXTENSIONS
Missing a(8) inserted by Colin Barker, Jan 15 2015
STATUS
approved