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.

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.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

V. Murali, FSRG, Rhodes University.

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

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

Cf. A007047, A107392.

Sequence in context: A226451 A185505 A051843 * A027942 A168214 A321421

Adjacent sequences: A107461 A107462 A107463 * A107465 A107466 A107467

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