Exploring patterns

Back from spring break, time to get chugging...

I am getting close to starting sequences and series with my kids, probably do that by the end of the week. I have my usual inquiry style group work put together from last year, but its pretty boring. Not as boring as me standing up in front of the kids for 2 periods, but not awesome. I want to find something more interesting to start with, then I'll go back to what I did (successfully) last year.

I've been searching the inter-webs for ideas. Patterns the kids can build or observe on the desk in front of them. I see the usual suspects of the sea shells and Fibonacci...

The curve doesn't fit... How am I suppose to convince students it does? And why would I?

Textbooks suggest the always exciting interest rate based problems. I can already see the eye lids drooping and the drool starting to flow. The books also had some brick stacking problems (which might work) or the oh-so inspiring stadium seating problems...

I'm looking for something that can be posed as a challenge to create something that's not 100% obvious. I want the kids to create something, have I said that yet? So far my candidates are:

1. Sphere stacking - Stack x number of spheres to create the tallest structure.
2. Packing circles (creative I know) - start with one penny, completely surround it, surround those...
3. Dilution of liquid - dy/dan style I love the potential to explore the idea of limits
4. Mowing lawn or harvesting hay in increasing or decreasing circles 
5. Stacking blocks - Stack x number of blocks on top of a single block to create the shortest possible structure 
6. Creating a spiral out of square blocks 

I want 3-5 good ones. So the students can explore multiple different patterns. There also needs to be a level of engagement, something my textbooks simply don't have.

I may also explore going in different directions. Such as giving an equation and asking them to create a visual representation of the pattern. This could be done with linear, quadratic equations even exponential...

Another option would be for me to create a pattern on paper, have the students expand the pattern and create a mathematical model...

Any thoughts and particularly any ideas would be greatly appreciated.