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Search: id:A107392
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| A107392 |
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Number of (inequivalent) fuzzy subgroups of the direct sum of group of integers modulo p^n and group of integers modulo 2 for a prime p with (p,2) = 1. Z_{p^n} + Z_2. |
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+0
5
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| 7, 31, 103, 303, 831, 2175, 5503, 13567, 32767, 77823, 182271, 421887, 966655, 2195455, 4947967
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This is just one row of a double sequence a(n,m) for n = 0,1,2, ... and m =0,1,2,... a(n,m) = ((2^(n+m+1))*(sum from r=0 to m of ( 2^(-r) * ( n choose (n-r))* (m choose r)))-1, with 0<= m <= n and a(0,0)=1
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REFERENCES
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V. Murali and B.B. Makamba, Fuzzy subgroups of finite abelian groups, Far East Journal of Mathematical Sciences (FJMS), Vol. 14, No. 1 (2004), pp. 113-125.
V. Murali and B.B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order p^n q^m, Fuzzy Sets And Systems, Vol. 144, No.3 (2004), pp. 459-470.
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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)*(n^2 + 7n + 8) -1
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EXAMPLE
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a(3) = 303. A fuzzy subgroup is simply a chain of subgroups in the lattice of subgroups. Counting the number of chains in the lattice of subgroups of Z_{p^3}+Z_2 gives us a(3)=303. The two papers cited describe the counting process using fuzzy subgroup concept.
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CROSSREFS
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Sequence in context: A118935 A055899 A139876 this_sequence A054497 A119359 A055366
Adjacent sequences: A107389 A107390 A107391 this_sequence A107393 A107394 A107395
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KEYWORD
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full,nonn,fini
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AUTHOR
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Venkat Murali (v.murali(AT)ru.ac.za), May 25 2005
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 08 2006
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