This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A107392 #29 Dec 18 2019 00:54:28
%S A107392 7,31,103,303,831,2175,5503,13567,32767,77823,182271,421887,966655,
%T A107392 2195455,4947967,11075583,24641535,54525951,120061951,263192575,
%U A107392 574619647,1249902591,2709520383,5855248383,12616466431,27111981055,58116276223,124285616127
%N A107392 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.
%C A107392 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_{r=0..m} (2^(-r) * binomial(n, n-r)* binomial(m, r))) - 1, with 0 <= m <= n and a(0,0)=1.
%H A107392 Colin Barker, <a href="/A107392/b107392.txt">Table of n, a(n) for n = 0..1000</a>
%H A107392 V. Murali, <a href="http://www.ru.ac.za/affiliates/fuzzysystems">FSRG, Rhodes University</a>.
%H A107392 V. Murali and B. B. Makamba, <a href="http://www.pphmj.com/abstract/500.htm">Fuzzy subgroups of finite Abelian groups</a>, Far East Journal of Mathematical Sciences (FJMS), Vol. 14, No. 1 (2004), pp. 113-125.
%H A107392 V. Murali and B. B. Makamba, <a href="http://dx.doi.org/10.1016/S0165-0114(03)00224-0">Counting the fuzzy subgroups of an Abelian group of order p^n q^m</a>, Fuzzy Sets And Systems, Vol. 144, No.3 (2004), pp. 459-470.
%H A107392 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8).
%F A107392 a(n) = (2^n)*(n^2 + 7n + 8) - 1 for n=0..14.
%F A107392 G.f.: (12*x^2 - 18*x + 7) / ((x-1)*(2*x-1)^3). - _Colin Barker_, Jan 15 2015
%e A107392 a(3) = 303. A fuzzy subgroup is simply a chain of subgroups in the lattice of subgroups. Counting 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.
%t A107392 LinearRecurrence[{7,-18,20,-8},{7,31,103,303},30] (* _Harvey P. Dale_, Dec 31 2015 *)
%o A107392 (PARI) Vec((12*x^2-18*x+7)/((x-1)*(2*x-1)^3) + O(x^100)) \\ _Colin Barker_, Jan 15 2015
%K A107392 nonn,easy
%O A107392 0,1
%A A107392 Venkat Murali (v.murali(AT)ru.ac.za), May 25 2005
%E A107392 Corrected by _T. D. Noe_, Nov 08 2006