Johnny,
It has been done here before. (Students, before asking questions, do a simple search using search function at bottom of the screen.) A search for "Washing Machine" would have turned up Ken Moore's complete well-documented Allen-Bradley Micrologix 1100 program (link below to Post # 124908, with both RSLogix program and pdf file), which should be easily adapted for any RSLogix-compatible PLC.
http://www.plctalk.net/qanda/showthread.php?t=12490&highlight=Washing+Machine
No, it does not use Sequencer instructions, just counters and timers. I would bet that you can't do it with fewer instructions using SQL instructions. You should be able to use this program as a starting point and pick out the steps that can be sequenced. The problem with Sequencers is that they are designed to do one step after another, regardless of conditions. We all know that there are always conditions that call for the sequence to be endlessly modified. Considering that, timers and counters are usually easier for programming, troubleshooting, and maintenance.
A typical "dumb" washing machine is certainly an example of a sequence of events that happen 1-2-3 regardless of modifying events. However, if you convert the simple mechanical timer and drum switch (of past older model washers) to PLC logic, you suddenly realize that it no longer make senses to keep the machine "dumb". What if the water does not fill all the way to the proper level (trash in the inlet valve)? What if the water is cold when it should be hot? What if the load becomes unbalanced? Do you still run the cycle, knowing that the clothes won't be clean, or do you set off an alarm and stop the machine until the problem is corrected? If the logic is no longer a series of dumb 1-2-3 steps, is it still sensible and practical to use a Sequencer instruction?